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Kombinatorik & Graphentheorie » Graphentheorie » Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5
Thema eröffnet 2016-02-17 22:35 von Slash
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Kein bestimmter Bereich Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5
haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2360, eingetragen 2022-05-04

offenbar verliert man bei dieser operation beim 4/8er immer den mittleren punkt... also bräuchte man auch beim 4/5er einen der in der mitte keinen knoten hat


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2361, eingetragen 2022-05-06

extrem knapp an einem neuen 4hölzer kleinerem 4/10er vorbei 82-113 treffen sich eben leider nicht exakt das lohnt sich trotzdem anzuschauen! buttons drücken: -wenige (oder beliebige?) winkel -beweglich -extrapolieren 113 Knoten, 2×Grad 2, 110×Grad 4, 1×Grad 10, 0 Überschneidungen, 227 Kanten, minimal 0.99999999999998601119, maximal 1.00000000000000599520, Einsetzkanten=Beweglichkeit+4, einzustellende Kanten, Abstände und Winkel: |P11-P14|=1.00000000000000377476 |P24-P41|=0.99999999999999866773 |P5-P58|=1.00000000000000222045 |P44-P62|=0.99999999999998601119 |P22-P68|=1.00000000000000310862 |P101-P104|=1.00000000000000199840 $ %Eingabe war: % % %Eingabe zu: Fig.2a (2,4) mit 22 Knoten, Doppelkite % % % % % %P[1]=[280.657311745539,55.35577518138058]; P[2]=[245.50437274725633,109.8936168089684]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(9,1,2,93.95502437185979); M(134,9,1,185) ; L(8,9,134); L(135,9,8); Q(10,1,9,D,ab(135,9,134,8,"gedreht")); Q(7,1,6,ab(134,1,8,9,10,"gedreht"),D); L(11,10,8); L(12,7,6); M(14,11,8,75.3200212577404); M(13,14,11,185); L(15,13,14); L(137,15,14); Q(16,14,11,ab(137,14,13,15,"gedreht"),D); L(17,15,16); M(20,13,14,93.95502437185975); M(138,20,13,185.00000000000017) ; L(19,20,138); L(139,20,19); Q(21,13,20,D,ab(139,20,138,19,"gedreht")); M(136,17,15,229.47751218592984) ; L(140,17,136); Q(18,13,17,ab(138,13,19,20,21,"gedreht"),ab(140,17,136,"gedreht")); A(12,11,ab(136,11,13,14,15,16,17,18,19,20,21,"gedreht")); L(22,21,19); M(26,5,2,blauerWinkel); M(25,26,5,184.9999999999999); L(27,25,26); L(141,27,26); Q(28,26,5,ab(141,26,25,27,"gedreht"),D); L(29,27,28); M(32,25,26,93.95502437185985); M(142,32,25,185.00000000000003) ; L(31,32,142); M(23,31,142,185.00000000000006) ; L(144,31,23); Q(143,32,31,D,ab(144,31,23,"gedreht")); Q(33,25,32,D,ab(143,32,23,142,31,"gedreht")); M(24,29,27,229.4775121859298) ; L(145,29,24); Q(30,25,29,ab(142,25,23,31,32,33,"gedreht"),ab(145,29,24,"gedreht")); M(39,5,26,229.47751218592956) ; L(40,5,39); M(41,40,5,200.52248781407056); L(42,41,40); M(147,42,40,185.00000000000003) ; L(148,42,147); Q(146,41,42,D,ab(148,42,147,"gedreht")); M(36,39,5,229.47751218593024) ; M(149,36,39,185.0000000000001); L(35,149,36); L(150,35,36); L(38,35,150); Q(37,36,39,ab(150,36,149,35,38,"gedreht"),D); Q(34,40,39,ab(147,40,41,42,146,"gedreht"),ab(149,39,35,36,37,38,"gedreht")); Q(43,24,5,D,ab(146,5,34,35,36,37,38,39,40,41,42,"gedreht")); A(24,41); M(58,5,26,208.75255781553003); L(59,58,5); M(56,58,5,140.52248781407); L(57,58,56); M(152,56,57,245.00000000000017) ; L(153,56,152); Q(55,57,56,D,ab(153,56,152,"gedreht")); L(151,57,55); M(60,59,5,169.47751218593007) ; L(61,59,60); M(154,61,59,184.99999999999977); L(155,154,61); Q(62,61,60,ab(155,61,154,"gedreht"),D); Q(54,58,59,ab(152,58,151,55,56,57,"gedreht"),ab(154,59,60,61,62,"gedreht")); A(38,5,ab(151,5,54,55,56,57,58,59,60,61,62,"gedreht")); M(46,5,26,73.23007000146002) ; L(48,5,46); M(45,46,5,184.99999999999977) ; L(157,46,45); Q(47,48,46,D,ab(157,46,45,"gedreht")); L(49,48,47); M(156,49,47,140.52248781407013); L(158,156,49); M(52,45,46,276.0449756281407) ; M(159,52,45,184.99999999999937); L(51,159,52); L(160,51,52); Q(53,52,45,ab(160,52,159,51,"gedreht"),D); Q(50,49,45,ab(158,49,156,"gedreht"),ab(159,45,51,52,53,"gedreht")); Q(44,60,5,D,ab(156,5,45,46,47,48,49,50,51,52,53,"gedreht")); A(44,62); L(63,51,53); M(70,23,31,gruenerWinkel); M(69,70,23,185); L(71,69,70); M(64,71,69,184.99999999999994); L(162,64,71); Q(161,71,70,ab(162,71,64,"gedreht"),D); Q(72,70,23,ab(161,70,64,69,71,"gedreht"),D); M(68,22,19,100.26573042182423); L(163,68,22); A(69,22,ab(163,22,68,"gedreht")); M(65,64,71,298.8859959151518); L(164,64,65); L(67,164,65); M(90,67,65,125); M(84,90,67,124.99999999999997); L(166,84,90); Q(165,90,67,ab(166,90,84,"gedreht"),D); Q(91,67,65,ab(165,67,84,90,"gedreht"),D); Q(66,64,68,ab(164,64,65,67,84,90,91,"gedreht"),D); N(89,68,90); M(83,89,68,209.2641133844238); L(167,83,89); M(85,84,90,270.7774099964298) ; L(86,84,85); L(87,86,85); L(82,87,85); L(168,86,87); Q(88,89,84,ab(167,89,83,"gedreht"),ab(168,84,82,85,86,87,"gedreht")); M(93,63,51,214.32512854663594); M(92,93,63,185.00000000000006); L(94,92,93); L(170,94,93); Q(95,93,63,ab(170,93,92,94,"gedreht"),D); L(96,94,95); M(99,92,93,93.9550243718599); M(171,99,92,184.9999999999996) ; L(98,99,171); L(172,99,98); Q(100,92,99,D,ab(172,99,171,98,"gedreht")); Q(97,92,96,ab(171,92,98,99,100,"gedreht"),D); L(101,100,98); L(102,97,96); M(104,101,98,75.32002125774045); M(103,104,101,185.00000000000003); L(105,103,104); L(174,105,104); Q(106,104,101,ab(174,104,103,105,"gedreht"),D); L(107,105,106); M(110,103,104,93.95502437185993); M(175,110,103,184.99999999999983) ; L(109,110,175); L(176,110,109); Q(111,103,110,D,ab(176,110,175,109,"gedreht")); M(173,107,105,229.47751218593024) ; L(177,107,173); Q(108,103,107,ab(175,103,109,110,111,"gedreht"),ab(177,107,173,"gedreht")); A(102,101,ab(173,101,103,104,105,106,107,108,109,110,111,"gedreht")); L(169,111,109); M(77,83,88,89.22059876981552) ; L(78,77,83); M(75,77,78,80.52248781406988); L(76,77,75); M(179,75,76,245.00000000000017) ; L(180,75,179); Q(74,76,75,D,ab(180,75,179,"gedreht")); M(79,78,77,229.4775121859298) ; L(80,78,79); M(181,80,78,184.99999999999977); L(182,181,80); Q(81,80,79,ab(182,80,181,"gedreht"),D); Q(73,77,78,ab(179,77,74,75,76,"gedreht"),ab(181,78,79,80,81,"gedreht")); L(178,76,74); L(113,81,79); Q(112,63,83,ab(169,63,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,"gedreht"),ab(178,83,73,74,75,76,77,78,79,80,81,113,"gedreht")); %R(11,14); // oder R(11,16); %R(24,41); %R(5,58); // oder R(5,59); %R(44,62); %R(22,68); // oder R(22,69); %R(101,104); // oder R(101,106); % % % %Ende der Eingabe. % Streichholzgraphen mit pgfplots, TikZ/pgf % v3.1a %\documentclass[margin=5mm, tikz]{standalone} %\usetikzlibrary{angles, quotes, babel} \usetikzlibrary{spy}%<- Neu \tikzset{SpyStyle/.style={ spy using outlines={rectangle, magnification=3, width=7.5cm, height=3cm, connect spies} }}%<- Neu %\usepackage{pgfplots} %\usepgfplotslibrary{patchplots} %\pgfplotsset{compat=1.13} % Eingaben =========================== \def\DefaultTextposition{south} % south west % etc. \def\AusnahmeTextposition{north} \def\AusnahmeListe{1,4,16,57,66,106,113} % Möglichst eingeben: \xdef\BeliebigesVorhandenesKoordinatenpaar{{1.41272889269626489295,0.21056350063769405101}} % 0,0 \colorlet{Kantenfarbe}{gray} \colorlet{Punktfarbe}{red} \def\Beschriftung{\punktnummer} % \punktnummer oder {} leer \pgfplotsset{ x=12mm, y=12mm, % Maßstab % width=20cm, height=5cm, % oder Bildmaße } \tikzset{font=\scriptsize} % Schrift Punktnummern und Winkel % =========================== %Unterprogramm, das Mehrfachplatzierung (je nach Pfadanzahl) % von Punktbezeichnungen verhindert ======= \xdef\LstPN{0} \newif\ifDupe \pgfplotsset{avoid dupes/.code={\Dupefalse \xdef\anker{\DefaultTextposition} % Default \foreach \X in \LstPN {\pgfmathtruncatemacro{\itest}{ifthenelse(\X==\punktnummer,1,0)} \ifnum\itest=1 \global\Dupetrue \breakforeach \fi} \ifDupe % auskommentieren: \typeout{\punktnummer\space ist\space ein\space Duplikat!}% \xdef\punktnummer{} %löscht mehrfache Nummern %\pgfkeysalso{/tikz/opacity=1} % macht mehrfache Nummern unsichtbar \else \xdef\LstPN{\LstPN,\punktnummer} \typeout{\punktnummer\space ist\space neu\space mit\space urprgl.\space Anker=\anker} \foreach \X in \LstExcept {\ifnum\X=\punktnummer %\pgfkeysalso{/tikz/anchor=-90} \xdef\anker{\AusnahmeTextposition} \fi} \typeout{\punktnummer\space ist\space neu\space mit\space Anker=\anker} \fi}} % ============ \begin{document} \xdef\LstExcept{\AusnahmeListe} % Für Zeichnung der Winkel \pgfdeclarelayer{bg} % declare background layer \pgfsetlayers{bg,main} % set the order of the layers (main is the standard % Aliaswerte für Aliasplot (Winkelplot) \pgfmathsetmacro{\xAlias}{\BeliebigesVorhandenesKoordinatenpaar[0]} \pgfmathsetmacro{\yAlias}{\BeliebigesVorhandenesKoordinatenpaar[1]} %\xAlias, \yAlias \begin{tikzpicture}[SpyStyle] % Punkte und Kanten ======================== \begin{axis}[hide axis, colormap={kantenfarbe}{color=(Kantenfarbe) color=(Kantenfarbe)}, thick, % Kanten ] \addplot+[mark size=1.125pt, mark options={Punktfarbe}, table/row sep=newline, patch, % Plot-Typ patch type=polygon, vertex count=2, % damit nur Kanten, keine Flächen, gezeichnet werden % % Angabe der Verbindungskanten ===================== patch table with point meta={ Startpkt Endpkt colordata \\ 1 1 \\ 2 1 \\ 3 1 \\ 3 2 \\ 4 3 \\ 4 2 \\ 5 4 \\ 5 2 \\ 6 3 \\ 6 4 \\ 7 9 \\ 7 6 \\ 8 9 \\ 8 7 \\ 9 1 \\ 10 1 \\ 10 8 \\ 10 9 \\ 11 10 \\ 11 8 \\ 12 7 \\ 12 6 \\ 12 17 \\ 13 14 \\ 14 11 \\ 15 13 \\ 15 14 \\ 16 14 \\ 16 15 \\ 16 11 \\ 17 15 \\ 17 16 \\ 18 20 \\ 18 17 \\ 18 12 \\ 19 20 \\ 19 18 \\ 20 13 \\ 21 13 \\ 21 19 \\ 21 20 \\ 22 21 \\ 22 19 \\ 23 31 \\ 24 29 \\ 24 41 \\ 25 26 \\ 26 5 \\ 27 25 \\ 27 26 \\ 28 26 \\ 28 27 \\ 28 5 \\ 29 27 \\ 29 28 \\ 30 32 \\ 30 24 \\ 30 29 \\ 31 32 \\ 31 30 \\ 32 25 \\ 33 25 \\ 33 23 \\ 33 31 \\ 33 32 \\ 34 42 \\ 34 36 \\ 35 34 \\ 35 36 \\ 36 39 \\ 37 35 \\ 37 36 \\ 37 39 \\ 38 35 \\ 38 37 \\ 38 55 \\ 38 57 \\ 39 5 \\ 40 5 \\ 40 39 \\ 41 40 \\ 42 41 \\ 42 40 \\ 43 24 \\ 43 34 \\ 43 41 \\ 43 42 \\ 44 60 \\ 44 49 \\ 44 62 \\ 45 46 \\ 46 5 \\ 47 48 \\ 47 45 \\ 47 46 \\ 48 5 \\ 48 46 \\ 49 48 \\ 49 47 \\ 50 49 \\ 50 44 \\ 50 52 \\ 51 50 \\ 51 52 \\ 52 45 \\ 53 51 \\ 53 52 \\ 53 45 \\ 54 56 \\ 54 61 \\ 55 57 \\ 55 56 \\ 55 54 \\ 56 58 \\ 57 58 \\ 57 56 \\ 58 5 \\ 59 58 \\ 59 5 \\ 60 59 \\ 61 59 \\ 61 60 \\ 62 61 \\ 62 54 \\ 62 60 \\ 63 51 \\ 63 53 \\ 64 71 \\ 65 64 \\ 66 64 \\ 66 65 \\ 66 68 \\ 67 66 \\ 67 65 \\ 68 22 \\ 69 70 \\ 69 22 \\ 69 68 \\ 70 23 \\ 71 69 \\ 71 70 \\ 72 64 \\ 72 70 \\ 72 71 \\ 72 23 \\ 73 75 \\ 73 80 \\ 74 76 \\ 74 75 \\ 74 73 \\ 75 77 \\ 76 77 \\ 76 75 \\ 77 83 \\ 78 77 \\ 78 83 \\ 79 78 \\ 80 78 \\ 80 79 \\ 81 80 \\ 81 73 \\ 81 79 \\ 82 87 \\ 82 85 \\ 83 89 \\ 84 90 \\ 85 84 \\ 86 84 \\ 86 85 \\ 87 86 \\ 87 85 \\ 88 83 \\ 88 89 \\ 88 86 \\ 88 87 \\ 89 68 \\ 89 90 \\ 90 67 \\ 91 67 \\ 91 84 \\ 91 90 \\ 91 65 \\ 92 93 \\ 93 63 \\ 94 92 \\ 94 93 \\ 95 93 \\ 95 94 \\ 95 63 \\ 96 94 \\ 96 95 \\ 97 99 \\ 97 96 \\ 98 99 \\ 98 97 \\ 99 92 \\ 100 92 \\ 100 98 \\ 100 99 \\ 101 100 \\ 101 98 \\ 102 97 \\ 102 96 \\ 102 107 \\ 103 104 \\ 104 101 \\ 105 103 \\ 105 104 \\ 106 104 \\ 106 105 \\ 106 101 \\ 107 105 \\ 107 106 \\ 108 110 \\ 108 107 \\ 108 102 \\ 109 110 \\ 109 108 \\ 110 103 \\ 111 103 \\ 111 109 \\ 111 110 \\ 112 109 \\ 112 111 \\ 112 74 \\ 112 76 \\ 113 81 \\ 113 79 \\ }, % % Beschriftung visualization depends on={value \thisrowno{0} \as \punktnummer}, every node near coord/.append style={ /pgfplots/avoid dupes,% Methode für Mehrfachplatzierung anwenden }, nodes near coords={\Beschriftung}, nodes near coords style={ anchor=\anker, text=black, %font=\scriptsize, name=p-\punktnummer, % Punkte bennennen path picture={% Jedem Punkt als Koordinate zuordnen: \coordinate[] (P\punktnummer) at (p-\punktnummer.\anker);} }, ] % Koordinatentabelle table[header=true, x index=1, y index=2, row sep=\\] { Nr x y \\ 0 0 0 \\% 0 Aliaspunkt 1 5.55351754842615719099 7.13343545726328809309 \\ 2 5.01174728742160890960 7.97396206855591316298 \\ 3 4.55471501998762118291 7.08451195386473653315 \\ 4 4.01294475898307467787 7.92503856515736249122 \\ 5 4.46997702641706240456 8.81448867984853734470 \\ 6 3.55591249154908561891 7.03558845046618586139 \\ 7 3.85298310213389694212 6.08073293661774716412 \\ 8 4.73395027646043686786 5.60755555152933116148 \\ 9 4.70325032528002573429 6.60708419694051762860 \\ 10 5.58421749960656654821 6.13390681185210073778 \\ 11 5.61491745078697679361 5.13437816644091515883 \\ 12 2.87751866490509877750 6.30088999805776595053 \\ 13 4.13048086045979356840 3.79406178241145930485 \\ 14 4.87269915562338074011 4.46421997442618412322 \\ 15 3.92121598920258351839 4.77192077718407059450 \\ 16 4.66343428436617646327 5.44207896919879807740 \\ 17 3.71195111794537524474 5.74977977195668188415 \\ 18 2.81745943533631226785 5.30269518293217867466 \\ 19 2.49245736669286044318 4.35698187786691004675 \\ 20 3.47397014789805114177 4.54837848267181765749 \\ 21 3.14896807925459709665 3.60266517760654947367 \\ 22 2.16745529804940462171 3.41126857280164186292 \\ 23 1.51787036240646000529 6.33675418831118264507 \\ 24 1.53632665236079013482 9.31228125617845492457 \\ 25 3.33801568013841043481 7.16565166227189997983 \\ 26 3.90399635327773708582 7.99007017106021866226 \\ 27 2.90703864474730355738 8.06801455765573294343 \\ 28 3.47301931788663065248 8.89243306644405073769 \\ 29 2.47606160935619978858 8.97037745303956413068 \\ 30 1.71009675168970409764 8.32749500902670902747 \\ 31 1.61398355704808205147 7.33212459866894494809 \\ 32 2.52405621591405715520 7.74657333564930272729 \\ 33 2.42794302127243577516 6.75120292529154131245 \\ 34 2.66828799863944121640 10.96111827375509228943 \\ 35 3.57836065750541676422 11.37556701073545184499 \\ 36 3.48224746286379538418 10.38019660037769043015 \\ 37 4.39232012172977004383 10.79464533735804820935 \\ 38 4.48843331637139186796 11.79001574771581317691 \\ 39 4.29620692708814910787 9.79927492700028501815 \\ 40 3.53024206942165319489 9.15639248298742991494 \\ 41 2.53328436089122055463 9.23433686958294153158 \\ 42 3.09926503403054676156 10.05875537837126110219 \\ 43 2.10230732550011456539 10.13669976496677449518 \\ 44 7.40957674843082347849 9.27585127107836626692 \\ 45 5.58139759240858701617 7.15173664617331894533 \\ 46 5.02568730941282559854 7.98311266301092903319 \\ 47 6.02353520158919497618 8.04868387681069386019 \\ 48 5.46782491859343355856 8.88005989364830305988 \\ 49 6.46567281076980471255 8.94563110744806877506 \\ 50 7.22360383014600593299 8.29329640051661165501 \\ 51 7.30736214431125663538 7.29681030186385193304 \\ 52 6.40250071127729469822 7.72251652334496618835 \\ 53 6.48625902544254806514 6.72603042469220557820 \\ 54 6.29815618243930952502 10.93860330475357756086 \\ 55 5.39329474940535114058 11.36430952623469536888 \\ 56 5.47705306357059740208 10.36782342758193564691 \\ 57 4.57219163053663901763 10.79352964906305167858 \\ 58 4.65594994470188527913 9.79704355041029550932 \\ 59 5.41388096407808561139 9.14470884347883128385 \\ 60 6.41172885625445410085 9.21028005727859166996 \\ 61 5.85601857325869712412 10.04165607411620264600 \\ 62 6.85386646543506738993 10.10722728791596303211 \\ 63 7.39112045847650911412 6.30032420321109398742 \\ 64 0.00000000000000000000 5.03442183329266423897 \\ 65 0.07873018357750834195 4.03752587172302668250 \\ 66 0.90270231943817536013 4.60415619153058042201 \\ 67 0.98143250301568318861 3.60726022996094242146 \\ 68 1.19590605361039936660 3.64810620838771892949 \\ 69 1.88678808481968207644 4.37107371730643645691 \\ 70 1.70232922361307159598 5.35391395280880910690 \\ 71 0.94339404240984203742 4.70274777529955034794 \\ 72 0.75893518120323044673 5.68558801080192299793 \\ 73 3.40161375919789277233 0.00000000000000000000 \\ 74 4.30790992126806404627 0.42264319066664096658 \\ 75 3.48874210037915810645 0.99619709503842901466 \\ 76 4.39503826244932938039 1.41884028570506814937 \\ 77 3.57587044156042299647 1.99239419007685625296 \\ 78 2.58952466660909941254 1.82770656991167967931 \\ 79 2.00112677965268170865 1.01913503527468551901 \\ 80 2.99556921290349675857 0.91385328495584161601 \\ 81 2.40717132594707816651 0.10528175031884658142 \\ 82 1.24503453359956184343 0.31681941154581227948 \\ 83 2.94007389133291541228 2.76425087801756541595 \\ 84 0.23619055073252198662 2.04373394858375379002 \\ 85 0.74061254216604222034 1.18027668006478214657 \\ 86 1.23617747606903205515 2.04884757313323273564 \\ 87 1.74059946750255178927 1.18539030461426198038 \\ 88 2.23616440140554262328 2.05396119768271256945 \\ 89 1.97299023915331783741 3.01870953809219022546 \\ 90 1.06016268659319101708 2.61036426839130486499 \\ 91 0.15746036715501690595 3.04062991015338912604 \\ 92 8.51325836983237316247 4.64478607079072247643 \\ 93 7.95218941415444557919 5.47255513700091000828 \\ 94 7.51585485218846471867 4.57277063500392699780 \\ 95 6.95478589651053269449 5.40053970121410920058 \\ 96 6.51845133454455716304 4.50075519921712885463 \\ 97 6.83753085982357244887 3.55302725484294290581 \\ 98 7.72920817203397358952 3.10035566208585899872 \\ 99 7.67539461482797236158 4.09890666281683557770 \\ 100 8.56707192703837172587 3.64623507005975389106 \\ 101 8.62088548424437028928 2.64768406932877420346 \\ 102 5.85723462147961537738 3.75056025231093226324 \\ 103 7.16785129539867593707 1.27338728695404346247 \\ 104 7.89436838982152533362 1.96053567814140539127 \\ 105 6.93602187967223660081 2.24614374260157312335 \\ 106 7.66253897409508599736 2.93329213378893793873 \\ 107 6.70419246394579904091 3.21890019824910034174 \\ 108 5.82028242971775267023 2.75124321776984226418 \\ 109 5.51724425652799332909 1.79826479955156393054 \\ 110 6.49406686255821608000 2.01231525236194119799 \\ 111 6.19102868936845762704 1.05933683414366441866 \\ 112 5.21420608333823576430 0.84528638133328193316 \\ 113 1.41272889269626489295 0.21056350063769405101 \\ 114 8.72 0 0 \\ }; % =================================== % Zeichnung der Dreiecke ===================== \addplot[no marks, % Aliasplot nodes near coords={},% Aliasplot visualization depends on={value \thisrowno{0} \as \PunktI}, visualization depends on={value \thisrowno{1} \as \PunktII}, visualization depends on={value \thisrowno{2} \as \PunktIII}, nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte path picture={%\pgftransformreset % Winkel zeichnen \begin{pgfonlayer}{bg} % 'select the background layer' für die Winkel \fill[black!10] (p-\PunktI) -- (p-\PunktII) -- (p-\PunktIII) ; \end{pgfonlayer} }},% ] table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen Punkt1 Punkt2 Punkt3 }; % Zeichnung der Winkel ===================== \addplot[no marks, % Aliasplot nodes near coords={},% Aliasplot visualization depends on={value \thisrowno{0} \as \PunktI}, visualization depends on={value \thisrowno{1} \as \Scheitel}, visualization depends on={value \thisrowno{2} \as \PunktII}, visualization depends on={value \thisrowno{3} \as \Winkelradius}, visualization depends on={value \thisrowno{4} \as \Winkelfarbe}, visualization depends on={value \thisrowno{5} \as \Winkelname}, visualization depends on={value \thisrowno{6} \as \WinkelExzentrizitaet}, nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte path picture={%\pgftransformreset % Winkel zeichnen \begin{pgfonlayer}{bg} % 'select the background layer' für die Winkel \draw pic [angle radius=\Winkelradius cm,% fill=\Winkelfarbe!40, draw=\Winkelfarbe,%<- Winkel färben / zeichnen %-latex, %<- Winkel mit Pfeil "$\Winkelname$", angle eccentricity =\WinkelExzentrizitaet, text=\Winkelfarbe% ] {angle = P\PunktI--P\Scheitel--P\PunktII}; \end{pgfonlayer} }},% ] table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen Punkt1 Scheitel Punkt2 Winkelradius[cm] Winkelfarbe Winkelname WinkelExz 2 5 26 0.45 Blue {} 1.5 \\ 31 23 70 0.45 Green {} 1.5 \\ }; \end{axis} % Annotationen %\node[above=3mm, align=center, font=\tiny] at (P11) {Wichtiger \\ Punkt}; %\draw[purple, very thick] (P8) -- (P10) node[near start, below, align=center, font=\tiny]{Wichtige \\ Kante}; %\begin{pgfonlayer}{bg} %\fill[yellow] (P12) -- (P13) -- (P14) -- cycle; %\end{pgfonlayer} %\foreach \n in \AusnahmeListe %\draw[cyan] (P\n) circle (3pt) %\if\n4 node[anchor=north west, font=\tiny, align=left]{Default-\\position \\ ge{\"a}ndert} \else\fi ; %\spy [red] on (P5) in node at (2.5,-1.25); %einzustellende Kanten, Abstände und Winkel: \draw[green,very thick] (P11) -- (P14); \draw[green,very thick] (P24) -- (P41); \draw[green,very thick] (P5) -- (P58); \draw[green,very thick] (P44) -- (P62); \draw[green,very thick] (P22) -- (P68); \draw[green,very thick] (P101) -- (P104); %nicht passende Kanten: \end{tikzpicture} \end{document} $


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  Beitrag No.2362, vom Themenstarter, eingetragen 2022-05-06

Ich habe ihn jetzt nicht neu eingegeben. Aber wenn der Abzählreim passt, dann müsste der Graph auch möglich sein. 112 Knoten, 111×Grad 4, 1×Grad 10, 0 Überschneidungen, 227 Kanten, minimal 0.98843873754576394575, maximal 1.00000000000002398082, Einsetzkanten=Beweglichkeit+6, einzustellende Kanten, Abstände und Winkel: |P22-P68|=1.00000000000000111022 |P82-P79|=0.99999999999999644729 |P82-P81|=0.98843873754576394575 |P11-P14|=1.00000000000000199840 |P24-P41|=0.99999999999999744649 |P5-P58|=0.99999999999999911182 |P44-P62|=1.00000000000002398082 |P101-P104|=1.00000000000000111022 nicht passende Kanten: |P82-P81|=0.98843873754576394575 $ %Eingabe war: % %Automatisch generierte Eingabe zu: %Eingabe zu: Fig.2a (2,4) mit 22 Knoten, Doppelkite % % % % % %P[1]=[251.81618510930033,176.13611562862258]; P[2]=[228.70673370929083,211.48483941063193]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(9,1,2,93.95502437185979); M(134,9,1,185.00000000000009) ; L(8,9,134); L(135,9,8); Q(10,1,9,D,ab(135,9,134,8,"gedreht")); Q(7,1,6,ab(134,1,8,9,10,"gedreht"),D); L(11,10,8); L(12,7,6); M(14,11,8,75.3200212577404); M(13,14,11,184.9999999999999); L(15,13,14); L(137,15,14); Q(16,14,11,ab(137,14,13,15,"gedreht"),D); L(17,15,16); M(20,13,14,93.95502437185976); M(138,20,13,185.0000000000002) ; L(19,20,138); L(139,20,19); Q(21,13,20,D,ab(139,20,138,19,"gedreht")); M(136,17,15,229.47751218592984) ; L(140,17,136); Q(18,13,17,ab(138,13,19,20,21,"gedreht"),ab(140,17,136,"gedreht")); A(12,11,ab(136,11,13,14,15,16,17,18,19,20,21,"gedreht")); L(22,21,19); M(26,5,2,blauerWinkel); M(25,26,5,184.99999999999997); L(27,25,26); L(141,27,26); Q(28,26,5,ab(141,26,25,27,"gedreht"),D); L(29,27,28); M(32,25,26,93.95502437185999); M(142,32,25,184.99999999999997) ; L(31,32,142); M(23,31,142,185.00000000000017) ; L(144,31,23); Q(143,32,31,D,ab(144,31,23,"gedreht")); Q(33,25,32,D,ab(143,32,23,142,31,"gedreht")); M(24,29,27,229.47751218592984) ; L(145,29,24); Q(30,25,29,ab(142,25,23,31,32,33,"gedreht"),ab(145,29,24,"gedreht")); M(39,5,26,229.47751218593015) ; L(40,5,39); M(41,40,5,200.52248781406962); L(42,41,40); M(147,42,40,185.00000000000003) ; L(148,42,147); Q(146,41,42,D,ab(148,42,147,"gedreht")); M(36,39,5,229.4775121859298) ; M(149,36,39,184.99999999999957); L(35,149,36); L(150,35,36); L(38,35,150); Q(37,36,39,ab(150,36,149,35,38,"gedreht"),D); Q(34,40,39,ab(147,40,41,42,146,"gedreht"),ab(149,39,35,36,37,38,"gedreht")); Q(43,24,5,D,ab(146,5,34,35,36,37,38,39,40,41,42,"gedreht")); A(24,41); M(58,5,26,208.75255781553028); L(59,58,5); M(56,58,5,140.52248781406993); L(57,58,56); M(152,56,57,245) ; L(153,56,152); Q(55,57,56,D,ab(153,56,152,"gedreht")); L(151,57,55); M(60,59,5,169.47751218592998) ; L(61,59,60); M(154,61,59,184.99999999999994); L(155,154,61); Q(62,61,60,ab(155,61,154,"gedreht"),D); Q(54,58,59,ab(152,58,151,55,56,57,"gedreht"),ab(154,59,60,61,62,"gedreht")); A(38,5,ab(151,5,54,55,56,57,58,59,60,61,62,"gedreht")); M(46,5,26,73.23007000145992) ; M(45,46,5,185.00000000000037) ; L(47,46,45); L(157,46,47); Q(48,5,46,D,ab(157,46,45,47,"gedreht")); L(49,48,47); M(156,49,47,140.52248781406965); L(158,156,49); M(52,45,46,276.0449756281399) ; M(159,52,45,185.0000000000001); L(51,159,52); L(160,51,52); Q(53,52,45,ab(160,52,159,51,"gedreht"),D); Q(50,49,45,ab(158,49,156,"gedreht"),ab(159,45,51,52,53,"gedreht")); Q(44,60,5,D,ab(156,5,45,46,47,48,49,50,51,52,53,"gedreht")); A(44,62); L(63,51,53); M(70,23,31,gruenerWinkel); M(69,70,23,185.00000000000006); L(71,69,70); M(64,71,69,184.99999999999991); L(162,64,71); Q(161,71,70,ab(162,71,64,"gedreht"),D); Q(72,70,23,ab(161,70,64,69,71,"gedreht"),D); M(68,22,19,100.26573042182449); L(163,68,22); A(69,22,ab(163,22,68,"gedreht")); M(65,64,71,298.88599591515145); L(164,64,65); L(67,164,65); M(90,67,65,125); M(84,90,67,124.99999999999997); L(166,84,90); Q(165,90,67,ab(166,90,84,"gedreht"),D); Q(91,67,65,ab(165,67,84,90,"gedreht"),D); Q(66,64,68,ab(164,64,65,67,84,90,91,"gedreht"),D); N(89,68,90); M(83,89,68,209.26411338442446); L(167,83,89); M(85,84,90,270.7774099964296) ; L(86,84,85); L(87,86,85); L(82,87,85); L(168,86,87); Q(88,89,84,ab(167,89,83,"gedreht"),ab(168,84,82,85,86,87,"gedreht")); M(93,63,51,214.3251285466361); M(92,93,63,184.9999999999994); L(94,92,93); L(170,94,93); Q(95,93,63,ab(170,93,92,94,"gedreht"),D); L(96,94,95); M(99,92,93,93.95502437186059); M(171,99,92,184.99999999999903) ; L(98,99,171); L(172,99,98); Q(100,92,99,D,ab(172,99,171,98,"gedreht")); Q(97,92,96,ab(171,92,98,99,100,"gedreht"),D); L(101,100,98); L(102,97,96); M(104,101,98,75.32002125774022); M(103,104,101,185.00000000000037); L(105,103,104); L(174,105,104); Q(106,104,101,ab(174,104,103,105,"gedreht"),D); L(107,105,106); M(110,103,104,93.9550243718592); M(175,110,103,185.00000000000057) ; L(109,110,175); L(176,110,109); Q(111,103,110,D,ab(176,110,175,109,"gedreht")); M(173,107,105,229.4775121859302) ; L(177,107,173); Q(108,103,107,ab(175,103,109,110,111,"gedreht"),ab(177,107,173,"gedreht")); A(102,101,ab(173,101,103,104,105,106,107,108,109,110,111,"gedreht")); L(169,111,109); M(77,83,88,89.22059876981695) ; L(78,77,83); M(75,77,78,80.52248781407015); L(76,77,75); M(179,75,76,245.00000000000023) ; L(180,75,179); Q(74,76,75,D,ab(180,75,179,"gedreht")); M(79,78,77,229.4775121859299) ; L(80,78,79); M(181,80,78,185.00000000000003); L(182,181,80); Q(81,80,79,ab(182,80,181,"gedreht"),D); Q(73,77,78,ab(179,77,74,75,76,"gedreht"),ab(181,78,79,80,81,"gedreht")); L(178,76,74); L(113,81,79); Q(112,63,83,ab(169,63,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,"gedreht"),ab(178,83,73,74,75,76,77,78,79,80,81,113,"gedreht")); %R(11,14); // oder R(11,16); %R(24,41); %R(5,58); // oder R(5,59); %R(44,62); %R(22,68); // oder R(22,69); %R(101,104); // oder R(101,106); %Z(113); %RA(82,79); RA(82,81); % %//von Button Feinjustieren ausgewählte Einsetzkanten: %R(11,14,"LightSlateGrey"); %R(24,41,"LightSlateGrey"); %R(5,58,"LightSlateGrey"); %R(44,62,"LightSlateGrey"); %R(101,104,"LightSlateGrey"); % %//von Button Feinjustieren ausgewählte Einsetzkanten: %R(11,14,"LightSlateGrey"); %R(24,41,"LightSlateGrey"); %R(5,58,"LightSlateGrey"); %R(44,62,"LightSlateGrey"); %R(101,104,"LightSlateGrey"); % %//von Button Feinjustieren ausgewählte Einsetzkanten: %R(82,81,"LightSlateGrey"); %R(11,14,"LightSlateGrey"); %R(24,41,"LightSlateGrey"); %R(5,58,"LightSlateGrey"); %R(44,62,"LightSlateGrey"); %R(101,104,"LightSlateGrey"); % %//von Button Feinjustieren ausgewählte Einsetzkanten: %R(82,81,"LightSlateGrey"); %R(11,14,"LightSlateGrey"); %R(24,41,"LightSlateGrey"); %R(5,58,"LightSlateGrey"); %R(44,62,"LightSlateGrey"); %R(101,104,"LightSlateGrey"); % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/5.53371853080728381968/7.07124341213488349922, 2/4.98652184469923120957/7.90824746631405250952, 3/4.53525341376353008371/7.01585920818823449707, 4/3.98805672765547747360/7.85286326236740350737, 5/4.43932515859117859947/8.74525152049322151981, 6/3.53678829671977723592/6.96047500424158638310, 7/3.84003010086279550350/6.00756136270837437507, 8/4.72404004652534403874/5.54009327185114841541, 9/4.68687431583503855137/6.53940238742162893715, 10/5.57088426149758753070/6.07193429656440386566, 11/5.60804999218789212989/5.07262518099392334392, 12/2.86316177761078671793/6.22140307759770028184, 13/4.13231560553549481796/3.72273332604713935723, 14/4.87018279886169214166/4.39767925352052913013, 15/3.91672888282578623986/4.69921802382344644400, 16/4.65459607615198400765/5.37416395129683888143, 17/3.70114216011607854995/5.67570272159975353077, 18/2.80956159771499880407/5.22284060047614318023, 19/2.49068459564144584206/4.27504449500377781135, 20/3.47093860162524503465/4.47278696326164038055, 21/3.15206159955169429310/3.52499085778927501167, 22/2.17180759356789288006/3.32724838953141155429, 23/1.50264362006845253461/6.24925402298857246564, 24/1.50264362006843943398/9.22483832968359251936, 25/3.31761262500983367119/7.08942514311952010075, 26/3.87846889180050480306/7.91733833180637081028, 27/2.88104690487417691713/7.98909751237536980284, 28/3.44190317166484849309/8.81701070106221962419, 29/2.44448118473852149535/8.88876988163121950492, 30/1.68251858897971451334/8.24114884841464601095, 31/1.59258110452408363500/7.24520143570160879420, 32/2.50006560699477375920/7.66528699576708305585, 33/2.41012812253914354699/6.66933958305404583911, 34/2.62435615364978414021/10.88066470705729571478, 35/3.53184065612047382032/11.30075026712276908825, 36/3.44190317166484316402/10.30480285440973098332, 37/4.34938767413553151187/10.72488841447520258043, 38/4.43932515859116350043/11.72083582718824068536, 39/4.25945018967990041148/9.72894100176216625186, 40/3.49748759392109631605/9.08131996854559453425, 41/2.50006560699476576559/9.15307914911459441498, 42/3.06092187378544045018/9.98099233780144601269, 43/2.06349988685911167607/10.05275151837044411707, 44/7.37600669711391532246/9.22483832968359074300, 45/5.56103769217252175139/7.08942514311951743622, 46/5.00018142538185017543/7.91733833180636903393, 47/5.99760341230817850544/7.98909751237536536195, 48/5.43674714551750781766/8.81701070106221962419, 49/6.43416913244383437132/8.88876988163121595221, 50/7.19613172820264246354/8.24114884841464423459, 51/7.28606921265827267575/7.24520143570160879420, 52/6.37858471018758166338/7.66528699576708305585, 53/6.46852219464321098741/6.66933958305404495093, 54/6.25429416353255440697/10.88066470705730992563, 55/5.34680966106185806552/11.30075026712277619367, 56/5.43674714551749982405/10.30480285440973631239, 57/4.52926264304680525896/10.72488841447520258043, 58/4.61920012750244346478/9.72894100176216802822, 59/5.38116272326125599790/9.08131996854559986332, 60/6.37858471018758432791/9.15307914911461040219, 61/5.81772844339690475834/9.98099233780145667083, 62/6.81515043032323486472/10.05275151837046543335, 63/7.37600669711390199978/6.24925402298856980110, 64/0.00000000000000000000/4.92938200227308787049, 65/0.10763629382059902717/3.93519166423284838530, 66/0.91481223585018545119/4.52550259807081278751, 67/1.02244852967078414530/3.53131226003057330232, 68/1.20105900796116804585/3.56734666845599202034, 69/1.89436450971813652444/4.28799046481693846289, 70/1.69850406489329408544/5.26862224390275457608, 71/0.94718225485906792915/4.60868623354501316669, 72/0.75132181003422604526/5.58931801263083016806, 73/3.37321721937416363346/0.00000000000000000000, 74/4.29199002829226383682/0.39478668365681413022, 75/3.49070832671060138352/0.99307393465786797382, 76/4.40948113562870158688/1.38786061831468177097, 77/3.60819943404703824541/1.98614786931573394924, 78/2.61728695459228255515/1.85163966116164080411, 79/2.00448602817735865855/1.06140233947592710351, 80/2.99525208698322176204/0.92581983058082029103, 81/2.38245116056829964180/0.13558250889510689574, 82/1.40226852160966242167/0.26307028150544853329, 83/2.99625566904069051688/2.77704914537353086956, 84/0.32290888146179652640/1.94681098815236941491, 85/0.86258870153573041772/1.10494063482890769734, 86/1.32182990416986068105/1.99325224558447988699, 87/1.86150972424379390624/1.15138189226101972373, 88/2.32075092687792494672/2.03969350301659035907, 89/2.01993458005440507108/2.99337559128487296078, 90/1.13008482349138295042/2.53712192199033381712, 91/0.21527258764119841516/2.94100132619260890010, 92/8.50168239246278822918/4.59611935548540273544, 93/7.93884454478833934132/5.42268668923698804463, 94/7.50443515965832297354/4.52197114806377253871, 95/6.94159731198387941475/5.34853848181535518336, 96/6.50718792685386038244/4.44782294064213878926, 97/6.82829342817875240002/3.50077951132176901083, 98/7.72093673466125629545/3.05001579562142755009, 99/7.66498791032076809415/4.04844943340358831563, 100/8.55763121680327643048/3.59768571770324419035, 101/8.61358004114376285543/2.59925207992108120436, 102/5.84757700923773260371/3.69621570453965908598, 103/7.16348809311037992842/1.22185114255797810934, 104/7.88853406712707361237/1.91055161123952643720, 105/6.92957897864225458306/2.19410960930884124664, 106/7.65462495265894560248/2.88281007799039246109, 107/6.69566986417412834953/3.16636807605970060919, 108/5.81276193030734678047/2.69682193315669227474, 109/5.51176238375885496623/1.74319765023516159985, 110/6.48812501170886335444/1.95933653785733596919, 111/6.18712546516037420474/1.00571225493580440613, 112/5.21076283721036404017/0.78957336731362925963} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/303.17/595.88/0.4/Blue, 23/84.84/281.29/0.4/Green} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 7/9, 7/6, 8/9, 8/7, 9/1, 10/1, 10/8, 10/9, 11/10, 11/8, 12/7, 12/6, 12/17, 13/14, 14/11, 15/13, 15/14, 16/14, 16/15, 16/11, 17/15, 17/16, 18/20, 18/17, 18/12, 19/20, 19/18, 20/13, 21/13, 21/19, 21/20, 22/21, 22/19, 23/31, 24/29, 24/41, 25/26, 26/5, 27/25, 27/26, 28/26, 28/27, 28/5, 29/27, 29/28, 30/32, 30/24, 30/29, 31/32, 31/30, 32/25, 33/25, 33/23, 33/31, 33/32, 34/42, 34/36, 35/34, 35/36, 36/39, 37/35, 37/36, 37/39, 38/35, 38/37, 38/55, 38/57, 39/5, 40/5, 40/39, 41/40, 42/41, 42/40, 43/24, 43/34, 43/41, 43/42, 44/60, 44/49, 44/62, 45/46, 46/5, 47/46, 47/45, 48/5, 48/46, 48/47, 49/48, 49/47, 50/49, 50/44, 50/52, 51/50, 51/52, 52/45, 53/51, 53/52, 53/45, 54/56, 54/61, 55/57, 55/56, 55/54, 56/58, 57/58, 57/56, 58/5, 59/58, 59/5, 60/59, 61/59, 61/60, 62/61, 62/54, 62/60, 63/51, 63/53, 64/71, 65/64, 66/64, 66/65, 66/68, 67/66, 67/65, 68/22, 69/70, 69/22, 69/68, 70/23, 71/69, 71/70, 72/64, 72/70, 72/71, 72/23, 73/75, 73/80, 74/76, 74/75, 74/73, 75/77, 76/77, 76/75, 77/83, 78/77, 78/83, 79/78, 80/78, 80/79, 81/80, 81/73, 81/79, 82/87, 82/85, 82/79, 82/81, 83/89, 84/90, 85/84, 86/84, 86/85, 87/86, 87/85, 88/83, 88/89, 88/86, 88/87, 89/68, 89/90, 90/67, 91/67, 91/84, 91/90, 91/65, 92/93, 93/63, 94/92, 94/93, 95/93, 95/94, 95/63, 96/94, 96/95, 97/99, 97/96, 98/99, 98/97, 99/92, 100/92, 100/98, 100/99, 101/100, 101/98, 102/97, 102/96, 102/107, 103/104, 104/101, 105/103, 105/104, 106/104, 106/105, 106/101, 107/105, 107/106, 108/110, 108/107, 108/102, 109/110, 109/108, 110/103, 111/103, 111/109, 111/110, 112/109, 112/111, 112/74, 112/76} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,112} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-82) -- (p-81); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/303.17/595.88/0.4/Blue, 23/84.84/281.29/0.4/Green} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/333, 2/93, 3/333, 4/93, 5/310, 6/213, 7/182, 8/302, 9/182, 10/62, 11/302, 12/198, 13/341, 14/312, 15/132, 16/72, 17/357, 18/237, 19/221, 20/341, 21/281, 22/316, 23/71, 24/206, 25/355, 26/326, 27/146, 28/26, 29/10, 30/115, 31/175, 32/115, 33/295, 34/86, 35/115, 36/295, 37/295, 38/125, 39/295, 40/326, 41/206, 42/26, 43/86, 44/334, 45/185, 46/154, 47/274, 48/94, 49/170, 50/290, 51/5, 52/65, 53/245, 54/5, 55/65, 56/5, 57/245, 58/110, 59/214, 60/274, 61/214, 62/94, 63/94, 64/126, 65/126, 66/6, 67/66, 68/196, 69/311, 70/71, 71/191, 72/71, 73/322, 74/233, 75/113, 76/353, 77/338, 78/82, 79/83, 80/82, 81/262, 82/273, 83/18, 84/246, 85/273, 86/93, 87/33, 88/258, 89/138, 90/306, 91/246, 92/334, 93/94, 94/274, 95/214, 96/79, 97/319, 98/183, 99/183, 100/3, 101/303, 102/199, 103/254, 104/254, 105/134, 106/14, 107/358, 108/102, 109/102, 110/102, 111/282, 112/353} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2363, eingetragen 2022-05-06

ja wenn dann, aber der abzählreim geht eben nicht mehr, weil ein doppelkite aufgelöst wurde (die alte 89-67 gibt es ja nicht mehr) nicht passende kante 0.988 ungleich 1.000 , er ist schon sauber eingegeben du siehst dass gleich: um zu passen müsste 84-90-89 ein 180° winkel sein was möglicherweise retten könnte wäre das links-unten gebilde über P112 auch so aufzubauen wie es rund um P65 ausschaut denke ich jedenfals im ersten moment der abzählreim spricht aber auch eindeutig gegen diese idee, denn dann fehlt die nächste einsetzkante... und wir wollen ja langsam mal anfangen dem reim zu vertrauen??? EDIT flippt langsam aus, 4/10er braucht sechs EK, drei befinden sich in den oberen vier kites drei in den jeweiligen Krebsscheren, befindet sich gar keine EK in dem linken kite ? Ist der nicht eingepasst? Falls nein könnte er doch aufgelöst werden, oder?


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2364, eingetragen 2022-05-06

jetzt gelingt es nichtmal mehr mit PGF/TikZ zu übertragen verlängere ich nach rechts verschiebe ich das problem nur zum nächsten doppelkite, glaub nicht das sich das ausgehen kann https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-4-10-versuch.jpg


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2365, eingetragen 2022-05-07

Hab endlos viele EDIT Nachträge in meine letzten Beiträge nachgetragen...


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4173
Wohnort: Raun
  Beitrag No.2366, eingetragen 2022-05-07

Vorm Rückstand aufholen muss ich mal wieder einen großen Fehler ausbügeln, zu den Einsetzkanten vom Doppelkite. \quoteon(2022-04-30 07:00 - StefanVogel in Beitrag No. 2325) \quoteon(2022-04-29 12:16 - haribo in Beitrag No. 2322) man, das wird echte grundlagenforschung mit den einsetzkanten https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-einsetzkante-kite.JPG ... ein doppelkite hat EINE einsetzkante, und zwar kommen dafür alle blauen kanten in frage, dargestellt sind die blauen nur am zweiten kite, natürlich gildet symetrie also die linken entsprechenden kanten wären auch einsatzkanten, es ist egal welche davon weggenommen würde der doppelkite behält seine form-stabilität, \quoteoff Ja. \quoteoff Nein. Ich habe den Doppelkite nochmal mit Button "acos(1/4)" exakt gerechnet und erhalte folgende Einsetzkanten, hellblau markiert, 22 Stück. Diese Kanten werden auf Zug oder Druck beansprucht, wenn eine davon geringfügig seine Länge ändern wollte, und der Graph bleibt starr, wenn man eine der hellblauen Kanten entfernt. 22 Knoten, 2×Grad 2, 20×Grad 4, 0 Überschneidungen, 42 Kanten, minimal 0.99999999999999900080, maximal 1.00000000000000066613, Einsetzkanten=Beweglichkeit+1, $ %Eingabe war: % %Doppelkite mit Button "acos(1/4)" gerechnet % % %P[1]=[64.46921762354003,99.16660002755097]; P[2]=[36.10960881176999,57.30330001377544]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); A(11,12,ab(5,12,[1,12]),Bew(2)); W(); % % %Belastungsarray=[ % [ // 0 % 1.154508497187474, // 1 (P1-P9) % -0.5590169943749475, // 2 (P1-P10) % 0., // 3 (P1-P2) % -1., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % -1., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0.8090169943749475, // 12 (P6-P7) % 5.640576474687263, // 13 (P7-P8) % 1.154508497187474, // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 5.640576474687263, // 18 (P8-P11) % -0.5590169943749475, // 19 (P10-P11) % 0.5590169943749475, // 20 (P11-P14) % -5.640576474687263, // 21 (P11-P16) % 5.854101966249685, // 22 (P7-P12) % -1.118033988749895, // 23 (P6-P12) % -5.854101966249685, // 24 (P12-P17) % 1.118033988749895, // 25 (P12-P18) % 1., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0.5590169943749475, // 28 (P13-P14) % -1.154508497187474, // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % -1.154508497187474, // 33 (P15-P17) % -5.640576474687263, // 34 (P16-P17) % -0.8090169943749475, // 35 (P17-P18) % 0., // 36 (P18-P19) % 1., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 0., // 43 % 0., // 44 % ], % [ // 1 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P19) % 0., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 1., // 43 % 0., // 44 % ], % [ // 2 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P19) % 0., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 0., // 43 % 1., // 44 % ], % ]; %Beweglichkeiten=[ % [ // 0 % 6.190242179999751, // 1 % 1.647433977800997, // 2 % 6.190242179999751, // 3 % 2.920456216543136, // 4 % 5.087772581666517, // 5 % 2.283945097172066, // 6 % 5.087772581666517, // 7 % 3.556967335914206, // 8 % 6.190242179999751, // 9 % 4.193478455285277, // 10 % 3.985302983333286, // 11 % 2.920456216543136, // 12 % 3.644621141666594, // 13 % 1.693866838189221, // 14 % 4.260920382916595, // 15 % 0.5799723792898495, // 16 % 4.917431660833173, // 17 % 1.670650407995109, // 18 % 5.53373090208317, // 19 % 0.5567559490957368, // 20 % 4.877219624166592, // 21 % -0.5339220796095228, // 22 % 2.752704500833288, // 23 % 2.602200656857601, // 24 % 2.36446211416666, // 25 % -0.9442782386557109, // 26 % 3.620840869166627, // 27 % -0.7391001591326167, // 28 % 2.81496206249994, // 29 % 0.2463667197108722, // 30 % 4.071340817499907, // 31 % 0.4515447992339663, // 32 % 3.26546201083322, // 33 % 1.437011678077456, // 34 % 2., // 35 % 1.575545137826334, // 36 % 1., // 37 % 0.7877725689131669, // 38 % 2.18223105708333, // 39 % 0.3156334495853114, // 40 % 1.18223105708333, // 41 % -0.4721391193278555, // 42 % 0., // 43 % 0., // 44 % ], % [ // 1 % -5.190242179999748, // 1 % -1.647433977800997, // 2 % -5.190242179999748, // 3 % -2.920456216543136, // 4 % -4.087772581666518, // 5 % -2.283945097172066, // 6 % -4.087772581666518, // 7 % -3.556967335914206, // 8 % -5.190242179999748, // 9 % -4.193478455285277, // 10 % -2.985302983333286, // 11 % -2.920456216543136, // 12 % -2.644621141666595, // 13 % -1.693866838189221, // 14 % -3.260920382916594, // 15 % -0.5799723792898495, // 16 % -3.917431660833172, // 17 % -1.670650407995109, // 18 % -4.533730902083171, // 19 % -0.5567559490957368, // 20 % -3.877219624166593, // 21 % 0.5339220796095228, // 22 % -1.752704500833288, // 23 % -2.602200656857601, // 24 % -1.36446211416666, // 25 % 0.9442782386557109, // 26 % -2.620840869166626, // 27 % 0.7391001591326167, // 28 % -1.81496206249994, // 29 % -0.2463667197108722, // 30 % -3.071340817499906, // 31 % -0.4515447992339663, // 32 % -2.26546201083322, // 33 % -1.437011678077456, // 34 % -1., // 35 % -1.575545137826334, // 36 % 0., // 37 % -0.7877725689131669, // 38 % -1.18223105708333, // 39 % -0.3156334495853114, // 40 % -0.1822310570833297, // 41 % 0.4721391193278555, // 42 % 1., // 43 % 0., // 44 % ], % [ // 2 % 0., // 1 % 1., // 2 % 0., // 3 % 1., // 4 % 0., // 5 % 1., // 6 % 0., // 7 % 1., // 8 % 0., // 9 % 1., // 10 % 0., // 11 % 1., // 12 % 0., // 13 % 1., // 14 % 0., // 15 % 1., // 16 % 0., // 17 % 1., // 18 % 0., // 19 % 1., // 20 % 0., // 21 % 1., // 22 % 0., // 23 % 1., // 24 % 0., // 25 % 1., // 26 % 0., // 27 % 1., // 28 % 0., // 29 % 1., // 30 % 0., // 31 % 1., // 32 % 0., // 33 % 1., // 34 % 0., // 35 % 1., // 36 % 0., // 37 % 1., // 38 % 0., // 39 % 1., // 40 % 0., // 41 % 1., // 42 % 0., // 43 % 1., // 44 % ], % ]; %Vergleichsrichtung=[[1,0,0],[2,1,0]]; %Nenner=152; %DD=[ % [37,37], % [43,43], % [44,44], % ]; % %Beweglichkeitsgrad=0; %Einsetzkantenzahl=1; %Maxi=24; Maxj=1; MaxInvAij=5513.645886938864; //=Kante [ 12, 17 ] %gerechnet_mit_Button="acos(1/4)"; % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.24/4.27, 2/1.12/2.61, 3/3.12/2.47, 4/1.99/0.82, 5/0.00/0.96, 6/3.99/0.67, 7/5.51/1.97, 8/5.69/3.96, 9/3.88/3.12, 10/4.06/5.11, 11/5.87/5.95, 12/5.87/0.00, 13/9.50/4.27, 14/7.69/5.11, 15/7.87/3.12, 16/6.05/3.96, 17/6.23/1.97, 18/7.76/0.67, 19/9.75/0.82, 20/8.63/2.47, 21/10.63/2.61, 22/11.75/0.96} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-1) -- (p-9); \draw[line width=2,blue!50] (p-1) -- (p-10); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-6) -- (p-3); \draw[line width=2,blue!50] (p-6) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-11) -- (p-8); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-11) -- (p-14); \draw[line width=2,blue!50] (p-11) -- (p-16); \draw[line width=2,blue!50] (p-12) -- (p-7); \draw[line width=2,blue!50] (p-12) -- (p-6); \draw[line width=2,blue!50] (p-12) -- (p-17); \draw[line width=2,blue!50] (p-12) -- (p-18); \draw[line width=2,blue!50] (p-13) -- (p-20); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-17) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-18); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 1/9, 1/10, 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 6/7, 8/7, 9/7, 9/8, 10/8, 10/9, 11/8, 11/10, 11/14, 11/16, 12/7, 12/6, 12/17, 12/18, 13/20, 13/21, 14/13, 15/13, 15/14, 16/14, 16/15, 17/15, 17/16, 17/18, 19/18, 20/18, 20/19, 21/19, 21/20, 22/19, 22/21} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/86, 2/86, 3/86, 4/206, 5/206, 6/190, 7/70, 8/355, 9/295, 10/175, 11/55, 12/230, 13/5, 14/5, 15/5, 16/125, 17/110, 18/214, 19/214, 20/214, 21/34, 22/334} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Alle anderen Kanten sind Anfügekanten. Dieses Ergebnis bedeutet, nicht nur allein die Flügelspitzen können entfernt werden, sondern auch Kanten wie P21-P13, P21-P19, P21-P2. Der verbleibende Restgraph behält dann die Eigenschaft, eine Einsetzkante zu enthalten. Ich versuche eine Erklärung, warum man beispielsweise Kanten P21-P13 als Anfügekante (ohne der wird der Graph beweglich) einstufen kann. Wenn man diese Kante entfernt 22 Knoten, 2×Grad 2, 2×Grad 3, 18×Grad 4, 0 Überschneidungen, 41 Kanten, minimal 0.99999999999999900080, maximal 1.00000000000000066613, Einsetzkanten=Beweglichkeit+0, $ %Eingabe war: % %Doppelkite mit Button "acos(1/4)" gerechnet % % %P[1]=[64.46921762354003,99.16660002755097]; P[2]=[36.10960881176999,57.30330001377544]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); A(11,12,ab(5,12,[1,12]),Bew(2)); W(); Z(13,21); % % %Belastungsarray=[ % [ // 0 % 1.154508497187474, // 1 (P1-P9) % -0.5590169943749475, // 2 (P1-P10) % 0., // 3 (P1-P2) % -1., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % -1., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0.8090169943749475, // 12 (P6-P7) % 5.640576474687263, // 13 (P7-P8) % 1.154508497187474, // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 5.640576474687263, // 18 (P8-P11) % -0.5590169943749475, // 19 (P10-P11) % 0.5590169943749475, // 20 (P11-P14) % -5.640576474687263, // 21 (P11-P16) % 5.854101966249685, // 22 (P7-P12) % -1.118033988749895, // 23 (P6-P12) % -5.854101966249685, // 24 (P12-P17) % 1.118033988749895, // 25 (P12-P18) % 1., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0.5590169943749475, // 28 (P13-P14) % -1.154508497187474, // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % -1.154508497187474, // 33 (P15-P17) % -5.640576474687263, // 34 (P16-P17) % -0.8090169943749475, // 35 (P17-P18) % 0., // 36 (P18-P19) % 1., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 0., // 43 % 0., // 44 % ], % [ // 1 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P19) % 0., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 1., // 43 % 0., // 44 % ], % [ // 2 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P19) % 0., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 0., // 43 % 1., // 44 % ], % ]; %Beweglichkeiten=[ % [ // 0 % 6.190242179999751, // 1 % 1.647433977800997, // 2 % 6.190242179999751, // 3 % 2.920456216543136, // 4 % 5.087772581666517, // 5 % 2.283945097172066, // 6 % 5.087772581666517, // 7 % 3.556967335914206, // 8 % 6.190242179999751, // 9 % 4.193478455285277, // 10 % 3.985302983333286, // 11 % 2.920456216543136, // 12 % 3.644621141666594, // 13 % 1.693866838189221, // 14 % 4.260920382916595, // 15 % 0.5799723792898495, // 16 % 4.917431660833173, // 17 % 1.670650407995109, // 18 % 5.53373090208317, // 19 % 0.5567559490957368, // 20 % 4.877219624166592, // 21 % -0.5339220796095228, // 22 % 2.752704500833288, // 23 % 2.602200656857601, // 24 % 2.36446211416666, // 25 % -0.9442782386557109, // 26 % 3.620840869166627, // 27 % -0.7391001591326167, // 28 % 2.81496206249994, // 29 % 0.2463667197108722, // 30 % 4.071340817499907, // 31 % 0.4515447992339663, // 32 % 3.26546201083322, // 33 % 1.437011678077456, // 34 % 2., // 35 % 1.575545137826334, // 36 % 1., // 37 % 0.7877725689131669, // 38 % 2.18223105708333, // 39 % 0.3156334495853114, // 40 % 1.18223105708333, // 41 % -0.4721391193278555, // 42 % 0., // 43 % 0., // 44 % ], % [ // 1 % -5.190242179999748, // 1 % -1.647433977800997, // 2 % -5.190242179999748, // 3 % -2.920456216543136, // 4 % -4.087772581666518, // 5 % -2.283945097172066, // 6 % -4.087772581666518, // 7 % -3.556967335914206, // 8 % -5.190242179999748, // 9 % -4.193478455285277, // 10 % -2.985302983333286, // 11 % -2.920456216543136, // 12 % -2.644621141666595, // 13 % -1.693866838189221, // 14 % -3.260920382916594, // 15 % -0.5799723792898495, // 16 % -3.917431660833172, // 17 % -1.670650407995109, // 18 % -4.533730902083171, // 19 % -0.5567559490957368, // 20 % -3.877219624166593, // 21 % 0.5339220796095228, // 22 % -1.752704500833288, // 23 % -2.602200656857601, // 24 % -1.36446211416666, // 25 % 0.9442782386557109, // 26 % -2.620840869166626, // 27 % 0.7391001591326167, // 28 % -1.81496206249994, // 29 % -0.2463667197108722, // 30 % -3.071340817499906, // 31 % -0.4515447992339663, // 32 % -2.26546201083322, // 33 % -1.437011678077456, // 34 % -1., // 35 % -1.575545137826334, // 36 % 0., // 37 % -0.7877725689131669, // 38 % -1.18223105708333, // 39 % -0.3156334495853114, // 40 % -0.1822310570833297, // 41 % 0.4721391193278555, // 42 % 1., // 43 % 0., // 44 % ], % [ // 2 % 0., // 1 % 1., // 2 % 0., // 3 % 1., // 4 % 0., // 5 % 1., // 6 % 0., // 7 % 1., // 8 % 0., // 9 % 1., // 10 % 0., // 11 % 1., // 12 % 0., // 13 % 1., // 14 % 0., // 15 % 1., // 16 % 0., // 17 % 1., // 18 % 0., // 19 % 1., // 20 % 0., // 21 % 1., // 22 % 0., // 23 % 1., // 24 % 0., // 25 % 1., // 26 % 0., // 27 % 1., // 28 % 0., // 29 % 1., // 30 % 0., // 31 % 1., // 32 % 0., // 33 % 1., // 34 % 0., // 35 % 1., // 36 % 0., // 37 % 1., // 38 % 0., // 39 % 1., // 40 % 0., // 41 % 1., // 42 % 0., // 43 % 1., // 44 % ], % ]; %Vergleichsrichtung=[[1,0,0],[2,1,0]]; %Nenner=152; %DD=[ % [37,37], % [43,43], % [44,44], % ]; % %Beweglichkeitsgrad=0; %Einsetzkantenzahl=1; %Maxi=24; Maxj=1; MaxInvAij=5513.645886938864; //=Kante [ 12, 17 ] %gerechnet_mit_Button="acos(1/4)"; % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.24/4.27, 2/1.12/2.61, 3/3.12/2.47, 4/1.99/0.82, 5/0.00/0.96, 6/3.99/0.67, 7/5.51/1.97, 8/5.69/3.96, 9/3.88/3.12, 10/4.06/5.11, 11/5.87/5.95, 12/5.87/0.00, 13/9.50/4.27, 14/7.69/5.11, 15/7.87/3.12, 16/6.05/3.96, 17/6.23/1.97, 18/7.76/0.67, 19/9.75/0.82, 20/8.63/2.47, 21/10.63/2.61, 22/11.75/0.96} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/9, 1/10, 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 6/7, 8/7, 9/7, 9/8, 10/8, 10/9, 11/8, 11/10, 11/14, 11/16, 12/7, 12/6, 12/17, 12/18, 13/20, 14/13, 15/13, 15/14, 16/14, 16/15, 17/15, 17/16, 17/18, 19/18, 20/18, 20/19, 21/19, 21/20, 22/19, 22/21} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,22} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/86, 2/86, 3/86, 4/206, 5/206, 6/190, 7/70, 8/355, 9/295, 10/175, 11/55, 12/230, 13/5, 14/5, 15/5, 16/125, 17/110, 18/214, 19/214, 20/94, 21/34, 22/334} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ dann bleiben zwei in gerader Linie verbundene Kanten P13-P20-18 übrig, an denen noch ein paar Kanten zu P19, P20, P21 frei in der Luft dranhängen. Eine geringe Krafteinwirkung auf eine diese Kanten würde eine sehr große (theoretisch unendlich große) Zugwirkung auf Doppelkante P13-P18 haben, ohne daß dadurch ein nutzbarer Bewegungsspielraum bei P20 entsteht. Man kann damit keinen Abstand variieren. Eine wirkliche Beweglichkeit erzeugt Entfernen von P21-P13 nicht. Andererseits, der Graph gilt auch nicht als statisch bestimmt. Es ist ein Zustand dazwischen. Zwecks Bestimmung von Einsetzkanten möchte ich diesen Zustand ebenfalls als beweglich bezeichnen, genauer als beweglich mit Beweglichkeitsspielraum 0. Klar, so eine Bezeichnung sieht allein für sich betrachtet komisch und widersprüchlich aus. Damit ließe sich aber sprachlich unterscheiden, daß es sich nicht um eine statisch bestimmte Konstellation handelt. Außerdem kann die Unterscheidung von Anfüge- und Einsetzkanten weiterhin dadurch erfolgen, ob sich bei Entfernen der Kante der Grad der Beweglichkeit ändert oder nicht, einschließlich der Beweglichkeit mit Bewegungsspielraum 0. Im Vergleich dazu, bei exakter Berechnung mit gerundeten Punktkoordinaten (Button "GAP") liegen die Kanten P13-P20-P18 nicht unbedingt exakt auf einer Linie. Dann wird eine Spannung in den Einsetzkanten auch in die Kanten zu P19, P21 übertragen, wenn die Einsetzkante geingfügig ihre Länge ändert. Nur die Flügelspitze 021-P22-P19 bleibt unbelastet. Ich markiere das mit gestrichelten hellblauen Linien. 22 Knoten, 2×Grad 2, 20×Grad 4, 0 Überschneidungen, 42 Kanten, minimal 0.99999999999999900080, maximal 1.00000000000000066613, Einsetzkanten=Beweglichkeit+1, $ %Eingabe war: % %Doppelkite mit Button "GAP" gerechnet % % %P[1]=[64.46921762354003,99.16660002755097]; P[2]=[36.10960881176999,57.30330001377544]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); A(11,12,ab(5,12,[1,12]),Bew(2)); W(); % % % %Belastungsarray=[ % [ // 0 % -1496493.846937006, // 1 (P1-P9) % 724606.9595131807, // 2 (P1-P10) % 0.3267134546758301, // 3 (P1-P2) % 1296217.047748086, // 4 (P1-P3) % -0.326713289978732, // 5 (P2-P3) % -0.3267130783924985, // 6 (P3-P4) % 0.3267130783924985, // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 1296215.88157845, // 10 (P3-P6) % 0.3267130783924985, // 11 (P4-P6) % -1048661.992922504, // 12 (P6-P7) % -7311399.178215584, // 13 (P7-P8) % -1496497.116029222, // 14 (P7-P9) % 3.269092556098601, // 15 (P8-P9) % 4.379878159107132, // 16 (P8-P10) % -3.269095642193928, // 17 (P9-P10) % -7311407.672944901, // 18 (P8-P11) % 724603.4881955446, // 19 (P10-P11) % -724611.063156813, // 20 (P11-P14) % 7311410.868029759, // 21 (P11-P16) % -7588184.560829499, // 22 (P7-P12) % 1449215.414003916, // 23 (P6-P12) % 7588183.998450038, // 24 (P12-P17) % -1449213.767889171, // 25 (P12-P18) % -1296215.657240261, // 26 (P13-P20) % -1.000001542955745, // 27 (P13-P21) % -724607.4413395916, // 28 (P13-P14) % 1496492.291034649, // 29 (P13-P15) % -4.787691473791624, // 30 (P14-P15) % 4.379884745912617, // 31 (P14-P16) % 4.787686954106755, // 32 (P15-P16) % 1496487.503348192, // 33 (P15-P17) % 7311404.039915922, // 34 (P16-P17) % 1048661.776174583, // 35 (P17-P18) % -1.000000308371063, // 36 (P18-P19) % -1296215.056955044, // 37 (P18-P20) % 1.000000308371063, // 38 (P19-P20) % -1.000000308371063, // 39 (P19-P21) % 1., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 0., // 43 % 0., // 44 % ], % [ // 1 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P19) % 0., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 1., // 43 % 0., // 44 % ], % [ // 2 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P19) % 0., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 0., // 43 % 1., // 44 % ], % ]; %Beweglichkeiten=[ % [ // 0 % 1.062599187950297, // 1 % 3.049294125121368, // 2 % 0.5312995939751483, // 3 % 3.409214267791583, // 4 % 0.4852494322261931, // 5 % 2.769135052195403, // 6 % -0.0460508034825599, // 7 % 3.129055194865618, // 8 % 0., // 9 % 3.769134410461798, // 10 % -0.09210096523151499, // 11 % 2.488975979269437, // 12 % 0.3234991936617255, // 13 % 1.999999358266395, // 14 % 0.962632493924387, // 15 % 1.942283121315246, // 16 % 0.6930491908060109, // 17 % 2.524646741693882, // 18 % 1.332181849335068, // 19 % 2.466930504742732, // 20 % 1.601765152453444, // 21 % 1.884567526097701, // 22 % -0.307767094339332, // 23 % 1.884567526097701, // 24 % 1.062599187950297, // 25 % 0.7198409270740348, // 26 % 1.332181849335068, // 27 % 1.302203905719066, // 28 % 0.6930491908060109, // 29 % 1.244488310501521, // 30 % 0.962632493924387, // 31 % 1.826851289146552, // 32 % 0.3234991936617255, // 33 % 1.769135693929007, // 34 % -0.09210096523151499, // 35 % 1.28015843119236, // 36 % -0.0460508034825599, // 37 % 0.6400792155961801, // 38 % 0.4852494322261931, // 39 % 1., // 40 % 0.5312995939751483, // 41 % 0.3599207844038198, // 42 % 0., // 43 % 0., // 44 % ], % [ // 1 % 1., // 1 % 0., // 2 % 1., // 3 % 0., // 4 % 1., // 5 % 0., // 6 % 1., // 7 % 0., // 8 % 1., // 9 % 0., // 10 % 1., // 11 % 0., // 12 % 1., // 13 % 0., // 14 % 1., // 15 % 0., // 16 % 1., // 17 % 0., // 18 % 1., // 19 % 0., // 20 % 1., // 21 % 0., // 22 % 1., // 23 % 0., // 24 % 1., // 25 % 0., // 26 % 1., // 27 % 0., // 28 % 1., // 29 % 0., // 30 % 1., // 31 % 0., // 32 % 1., // 33 % 0., // 34 % 1., // 35 % 0., // 36 % 1., // 37 % 0., // 38 % 1., // 39 % 0., // 40 % 1., // 41 % 0., // 42 % 1., // 43 % 0., // 44 % ], % [ // 2 % -1.062599187950297, // 1 % -2.049294125121368, // 2 % -0.5312995939751483, // 3 % -2.409214267791583, // 4 % -0.4852494322261931, // 5 % -1.769135052195403, // 6 % 0.0460508034825599, // 7 % -2.129055194865618, // 8 % 0., // 9 % -2.769134410461798, // 10 % 0.09210096523151499, // 11 % -1.488975979269438, // 12 % -0.3234991936617255, // 13 % -0.9999993582663952, // 14 % -0.962632493924387, // 15 % -0.9422831213152458, // 16 % -0.6930491908060109, // 17 % -1.524646741693882, // 18 % -1.332181849335068, // 19 % -1.466930504742732, // 20 % -1.601765152453444, // 21 % -0.8845675260977013, // 22 % 0.307767094339332, // 23 % -0.8845675260977013, // 24 % -1.062599187950297, // 25 % 0.2801590729259651, // 26 % -1.332181849335068, // 27 % -0.3022039057190657, // 28 % -0.6930491908060109, // 29 % -0.2444883105015212, // 30 % -0.962632493924387, // 31 % -0.826851289146552, // 32 % -0.3234991936617255, // 33 % -0.7691356939290075, // 34 % 0.09210096523151499, // 35 % -0.2801584311923602, // 36 % 0.0460508034825599, // 37 % 0.3599207844038198, // 38 % -0.4852494322261931, // 39 % 0., // 40 % -0.5312995939751483, // 41 % 0.6400792155961801, // 42 % 0., // 43 % 1., // 44 % ], % ]; %Vergleichsrichtung=[]; %Nenner=1000000; %DD=[ % [40,40], % [43,43], % [44,44], % ]; % %Beweglichkeitsgrad=0; %Einsetzkantenzahl=1; %Maxi=22; Maxj=10; MaxInvAij=28600880332266.71; //=Kante [ 7, 12 ] %gerechnet_mit_Button="GAP"; % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.24/4.27, 2/1.12/2.61, 3/3.12/2.47, 4/1.99/0.82, 5/0.00/0.96, 6/3.99/0.67, 7/5.51/1.97, 8/5.69/3.96, 9/3.88/3.12, 10/4.06/5.11, 11/5.87/5.95, 12/5.87/0.00, 13/9.50/4.27, 14/7.69/5.11, 15/7.87/3.12, 16/6.05/3.96, 17/6.23/1.97, 18/7.76/0.67, 19/9.75/0.82, 20/8.63/2.47, 21/10.63/2.61, 22/11.75/0.96} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-1) -- (p-9); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-1) -- (p-10); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-2) -- (p-1); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-3) -- (p-1); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-3) -- (p-2); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-4) -- (p-3); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-4) -- (p-2); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-6) -- (p-3); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-6) -- (p-4); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-6) -- (p-7); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-8) -- (p-7); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-9) -- (p-7); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-9) -- (p-8); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-10) -- (p-8); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-10) -- (p-9); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-11) -- (p-8); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-11) -- (p-10); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-11) -- (p-14); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-11) -- (p-16); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-12) -- (p-7); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-12) -- (p-6); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-12) -- (p-17); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-12) -- (p-18); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-13) -- (p-20); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-13) -- (p-21); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-14) -- (p-13); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-15) -- (p-13); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-15) -- (p-14); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-16) -- (p-14); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-16) -- (p-15); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-17) -- (p-15); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-17) -- (p-16); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-17) -- (p-18); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-19) -- (p-18); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-20) -- (p-18); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-20) -- (p-19); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-21) -- (p-19); \draw[line width=2,dash=on 4.00pt off 4.00pt phase 0.00pt,blue!50] (p-21) -- (p-20); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 1/9, 1/10, 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 6/7, 8/7, 9/7, 9/8, 10/8, 10/9, 11/8, 11/10, 11/14, 11/16, 12/7, 12/6, 12/17, 12/18, 13/20, 13/21, 14/13, 15/13, 15/14, 16/14, 16/15, 17/15, 17/16, 17/18, 19/18, 20/18, 20/19, 21/19, 21/20, 22/19, 22/21} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/86, 2/86, 3/86, 4/206, 5/206, 6/190, 7/70, 8/355, 9/295, 10/175, 11/55, 12/230, 13/5, 14/5, 15/5, 16/125, 17/110, 18/214, 19/214, 20/214, 21/34, 22/334} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Dann sind nur die Flügelspitzen Anfügekanten. Dieser Unterschied zwischen exakten und gerundeten Punktkoordinaten war bisher nie weiter wichtig gewesen. Doch jetzt für den Abzählreim mit Beweglichkeit und Einsetzkanten sollte die exakte Variante Ausgangspunkt sein. Dann hat der Doppelkite paar Anfügekanten mehr und das ist hoffentlich eine kleine Wiedergutmachung für den Fehler. Als Beispielgraph, wo die Kante P21-P13 entfernt ist, nehme ich den 4/2 mit 80 Kanten 41 Knoten, 2×Grad 2, 39×Grad 4, 0 Überschneidungen, 80 Kanten, minimal 0.99999999999999666933, maximal 1.00000000000000732747, Einsetzkanten=Beweglichkeit+1, $ %Eingabe war: % %Fig.2h #??? % % %P[1]=[239.66511164683388,150.42860859392886]; P[2]=[221.20904391435022,196.64239510676478]; %D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); A(11,12,ab(5,12,[1,7],9,10),Bew(2)); L(21,20,19); L(22,20,21); A(22,21,ab(20,21,[1,21],"gespiegelt"),Bew(2)); A(18,40,Bew(5)); R(18,40); % % %Belastungsarray=[ % [ // 0 % 1.154508497187474, // 1 (P1-P9) % -0.5590169943749475, // 2 (P1-P10) % 0., // 3 (P1-P2) % -1., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % -1., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0.8090169943749475, // 12 (P6-P7) % 5.640576474687263, // 13 (P7-P8) % 1.154508497187474, // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 5.640576474687263, // 18 (P8-P11) % -0.5590169943749475, // 19 (P10-P11) % 0.5590169943749475, // 20 (P11-P14) % -5.640576474687263, // 21 (P11-P16) % 5.854101966249685, // 22 (P7-P12) % -1.118033988749895, // 23 (P6-P12) % -5.854101966249685, // 24 (P12-P17) % 1.118033988749895, // 25 (P12-P18) % 1., // 26 (P13-P19) % 0., // 27 (P13-P20) % 0.5590169943749475, // 28 (P13-P14) % -1.154508497187474, // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % -1.154508497187474, // 33 (P15-P17) % -5.640576474687263, // 34 (P16-P17) % -0.8090169943749475, // 35 (P17-P18) % 0., // 36 (P18-P40) % 1., // 37 (P18-P19) % 0., // 38 (P19-P20) % 0., // 39 (P20-P21) % 0., // 40 (P19-P21) % 0., // 41 (P21-P41) % 0., // 42 (P20-P22) % 0., // 43 (P21-P22) % 0., // 44 (P22-P41) % 0., // 45 (P23-P31) % 0., // 46 (P23-P32) % 0., // 47 (P23-P24) % 0., // 48 (P23-P25) % 0., // 49 (P24-P25) % 0., // 50 (P24-P26) % 0., // 51 (P25-P26) % 0., // 52 (P24-P27) % 0., // 53 (P26-P27) % 0., // 54 (P25-P28) % 0., // 55 (P26-P28) % 0., // 56 (P28-P29) % 0., // 57 (P29-P30) % 0., // 58 (P29-P31) % 0., // 59 (P30-P31) % 0., // 60 (P30-P32) % 0., // 61 (P31-P32) % 0., // 62 (P30-P33) % 0., // 63 (P32-P33) % 0., // 64 (P33-P36) % 0., // 65 (P33-P38) % 0., // 66 (P28-P34) % 0., // 67 (P29-P34) % 0., // 68 (P34-P39) % 0., // 69 (P34-P40) % 0., // 70 (P35-P41) % 0., // 71 (P22-P35) % 0., // 72 (P35-P36) % 0., // 73 (P35-P37) % 0., // 74 (P36-P37) % 0., // 75 (P36-P38) % 0., // 76 (P37-P38) % 0., // 77 (P37-P39) % 0., // 78 (P38-P39) % 0., // 79 (P39-P40) % 0., // 80 (P40-P41) % 0., // 81 % 0., // 82 % ], % [ // 1 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P19) % 0., // 27 (P13-P20) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P40) % 0., // 37 (P18-P19) % 0., // 38 (P19-P20) % 0., // 39 (P20-P21) % 0., // 40 (P19-P21) % 0., // 41 (P21-P41) % 0., // 42 (P20-P22) % 0., // 43 (P21-P22) % 0., // 44 (P22-P41) % 1.154508497187474, // 45 (P23-P31) % -0.5590169943749475, // 46 (P23-P32) % 0., // 47 (P23-P24) % -1., // 48 (P23-P25) % 0., // 49 (P24-P25) % 0., // 50 (P24-P26) % 0., // 51 (P25-P26) % 0., // 52 (P24-P27) % 0., // 53 (P26-P27) % -1., // 54 (P25-P28) % 0., // 55 (P26-P28) % 0.8090169943749475, // 56 (P28-P29) % 5.640576474687263, // 57 (P29-P30) % 1.154508497187474, // 58 (P29-P31) % 0., // 59 (P30-P31) % 0., // 60 (P30-P32) % 0., // 61 (P31-P32) % 5.640576474687263, // 62 (P30-P33) % -0.5590169943749475, // 63 (P32-P33) % 0.5590169943749475, // 64 (P33-P36) % -5.640576474687263, // 65 (P33-P38) % -1.118033988749895, // 66 (P28-P34) % 5.854101966249685, // 67 (P29-P34) % -5.854101966249685, // 68 (P34-P39) % 1.118033988749895, // 69 (P34-P40) % 1., // 70 (P35-P41) % 0., // 71 (P22-P35) % 0.5590169943749475, // 72 (P35-P36) % -1.154508497187474, // 73 (P35-P37) % 0., // 74 (P36-P37) % 0., // 75 (P36-P38) % 0., // 76 (P37-P38) % -1.154508497187474, // 77 (P37-P39) % -5.640576474687263, // 78 (P38-P39) % -0.8090169943749475, // 79 (P39-P40) % 1., // 80 (P40-P41) % 0., // 81 % 0., // 82 % ], % [ // 2 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P19) % 0., // 27 (P13-P20) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P40) % 0., // 37 (P18-P19) % 0., // 38 (P19-P20) % 0., // 39 (P20-P21) % 0., // 40 (P19-P21) % 0., // 41 (P21-P41) % 0., // 42 (P20-P22) % 0., // 43 (P21-P22) % 0., // 44 (P22-P41) % 0., // 45 (P23-P31) % 0., // 46 (P23-P32) % 0., // 47 (P23-P24) % 0., // 48 (P23-P25) % 0., // 49 (P24-P25) % 0., // 50 (P24-P26) % 0., // 51 (P25-P26) % 0., // 52 (P24-P27) % 0., // 53 (P26-P27) % 0., // 54 (P25-P28) % 0., // 55 (P26-P28) % 0., // 56 (P28-P29) % 0., // 57 (P29-P30) % 0., // 58 (P29-P31) % 0., // 59 (P30-P31) % 0., // 60 (P30-P32) % 0., // 61 (P31-P32) % 0., // 62 (P30-P33) % 0., // 63 (P32-P33) % 0., // 64 (P33-P36) % 0., // 65 (P33-P38) % 0., // 66 (P28-P34) % 0., // 67 (P29-P34) % 0., // 68 (P34-P39) % 0., // 69 (P34-P40) % 0., // 70 (P35-P41) % 0., // 71 (P22-P35) % 0., // 72 (P35-P36) % 0., // 73 (P35-P37) % 0., // 74 (P36-P37) % 0., // 75 (P36-P38) % 0., // 76 (P37-P38) % 0., // 77 (P37-P39) % 0., // 78 (P38-P39) % 0., // 79 (P39-P40) % 0., // 80 (P40-P41) % 1., // 81 % 0., // 82 % ], % [ // 3 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P19) % 0., // 27 (P13-P20) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P40) % 0., // 37 (P18-P19) % 0., // 38 (P19-P20) % 0., // 39 (P20-P21) % 0., // 40 (P19-P21) % 0., // 41 (P21-P41) % 0., // 42 (P20-P22) % 0., // 43 (P21-P22) % 0., // 44 (P22-P41) % 0., // 45 (P23-P31) % 0., // 46 (P23-P32) % 0., // 47 (P23-P24) % 0., // 48 (P23-P25) % 0., // 49 (P24-P25) % 0., // 50 (P24-P26) % 0., // 51 (P25-P26) % 0., // 52 (P24-P27) % 0., // 53 (P26-P27) % 0., // 54 (P25-P28) % 0., // 55 (P26-P28) % 0., // 56 (P28-P29) % 0., // 57 (P29-P30) % 0., // 58 (P29-P31) % 0., // 59 (P30-P31) % 0., // 60 (P30-P32) % 0., // 61 (P31-P32) % 0., // 62 (P30-P33) % 0., // 63 (P32-P33) % 0., // 64 (P33-P36) % 0., // 65 (P33-P38) % 0., // 66 (P28-P34) % 0., // 67 (P29-P34) % 0., // 68 (P34-P39) % 0., // 69 (P34-P40) % 0., // 70 (P35-P41) % 0., // 71 (P22-P35) % 0., // 72 (P35-P36) % 0., // 73 (P35-P37) % 0., // 74 (P36-P37) % 0., // 75 (P36-P38) % 0., // 76 (P37-P38) % 0., // 77 (P37-P39) % 0., // 78 (P38-P39) % 0., // 79 (P39-P40) % 0., // 80 (P40-P41) % 0., // 81 % 1., // 82 % ], % ]; %Beweglichkeiten=[ % [ // 0 % -15.88893122804511, // 1 % 3.236278574967593, // 2 % -15.88893122804511, // 3 % 0.9684699169468072, // 4 % -13.92495131927682, // 5 % 2.102374245957201, // 6 % -13.92495131927682, // 7 % -0.1654344120635858, // 8 % -15.88893122804511, // 9 % -1.299338741073978, // 10 % -11.96097141050852, // 11 % 0.9684699169468072, // 12 % -11.35406824208816, // 13 % 3.1535613689358, // 14 % -12.4519663877006, // 15 % 5.137893944703988, // 16 % -13.62149973506664, // 17 % 3.194919971951696, // 18 % -14.71939788067907, // 19 % 5.179252547719884, // 20 % -13.54986453331303, // 21 % 7.122226520472176, // 22 % -9.765175119283647, // 23 % 1.535422081452005, // 24 % -9.073545845970084, // 25 % 7.85325008159757, // 26 % -11.31170518964156, // 27 % 7.487738301034871, // 28 % -9.876083030456043, // 29 % 5.732191341979219, // 30 % -12.11424237412752, // 31 % 5.36667956141652, // 32 % -10.678620214942, // 33 % 3.611132602360865, // 34 % -8.42427962510312, // 35 % 3.364343999708874, // 36 % -8.42427962510312, // 37 % 3.364343999708874, // 38 % -4.861406033418523, // 39 % 6.171078081743131, // 40 % -4.21213981255156, // 41 % 1.682171999854437, // 42 % -0.6492662208669635, // 43 % 4.488906081888692, // 44 % 5.322871951845022, // 45 % -5.234926789419333, // 46 % 3.760671448930856, // 47 % -6.878850661771323, // 48 % 3.11809186504343, // 49 % -4.703983404266833, // 50 % 1.555891362129264, // 51 % -6.347907276618824, // 52 % 2.198470946016689, // 53 % -8.522774534123311, // 54 % 0.9133117782418382, // 55 % -4.173040019114334, // 56 % 1.978590522060893, // 57 % -2.17100672584438, // 58 % 4.141377184617296, // 59 % -1.488870403939317, // 60 % 3.650731236952957, // 61 % -3.702966757631857, // 62 % 5.81351789950936, // 63 % -3.020830435726794, // 64 % 6.3041638471737, // 65 % -0.8067340820342543, // 66 % -0.2878605410426373, // 67 % -2.249464918220481, // 68 % 3.562873591684597, // 69 % 2.806734082034255, // 70 % 4.933518719429149, // 71 % 1., // 72 % 2.68351854263205, // 73 % 0.7163535408169783, // 74 % 4.054163670376601, // 75 % -1.090380541217276, // 76 % 1.804163493579502, // 77 % -1.374027000400297, // 78 % 0., // 79 % 0., // 80 % 0., // 81 % 0., // 82 % ], % [ // 1 % 12.65615406399194, // 1 % -0.438275681902027, // 2 % 12.65615406399194, // 3 % 1.829532976118758, // 4 % 10.69217415522365, // 5 % 0.6956286471083653, // 6 % 10.69217415522365, // 7 % 2.96343730512915, // 8 % 12.65615406399194, // 9 % 4.097341634139543, // 10 % 8.728194246455347, // 11 % 1.829532976118758, // 12 % 8.121291078034986, // 13 % -0.3555584758702346, // 14 % 9.219189223647424, // 15 % -2.339891051638421, // 16 % 10.38872257101346, // 17 % -0.3969170788861303, // 18 % 11.4866207166259, // 19 % -2.381249654654318, // 20 % 10.31708736925986, // 21 % -4.324223627406609, // 22 % 6.532397955230473, // 23 % 1.262580811613562, // 24 % 5.840768681916909, // 25 % -5.055247188532, // 26 % 8.07892802558839, // 27 % -4.689735407969306, // 28 % 6.643305866402868, // 29 % -2.934188448913653, // 30 % 8.881465210074342, // 31 % -2.568676668350955, // 32 % 7.445843050888826, // 33 % -0.8131297092952989, // 34 % 5.191502461049947, // 35 % -0.5663411066433097, // 36 % 5.42282691213453, // 37 % -2.165675404331831, // 38 % 3.129355225849646, // 39 % -3.972409486366085, // 40 % 2.711413456067265, // 41 % -1.082837702165916, // 42 % 0.4179417697823808, // 43 % -2.889571784200171, // 44 % -4.053470046445309, // 45 % 6.234926789419334, // 46 % -2.491269543531143, // 47 % 7.878850661771323, // 48 % -1.848689959643717, // 49 % 5.703983404266834, // 50 % -0.2864894567295512, // 51 % 7.347907276618823, // 52 % -0.9290690406169769, // 53 % 9.522774534123311, // 54 % 0.3560901271578754, // 55 % 5.173040019114334, // 56 % -0.7091886166611794, // 57 % 3.17100672584438, // 58 % -2.871975279217583, // 59 % 2.488870403939317, // 60 % -2.381329331553244, // 61 % 4.702966757631856, // 62 % -4.544115994109649, // 63 % 4.020830435726794, // 64 % -5.034761941773988, // 65 % 1.806734082034254, // 66 % 1.55726244644235, // 67 % 3.249464918220481, // 68 % -2.293471686284884, // 69 % -1.806734082034254, // 70 % -3.664116814029435, // 71 % 0., // 72 % -1.414116637232337, // 73 % 0.2836464591830217, // 74 % -2.784761764976888, // 75 % 2.090380541217276, // 76 % -0.5347615881797894, // 77 % 2.374027000400297, // 78 % 1.269401905399713, // 79 % 1., // 80 % 0., // 81 % 0., // 82 % ], % [ // 2 % 1., // 1 % 0., // 2 % 1., // 3 % 0., // 4 % 1., // 5 % 0., // 6 % 1., // 7 % 0., // 8 % 1., // 9 % 0., // 10 % 1., // 11 % 0., // 12 % 1., // 13 % 0., // 14 % 1., // 15 % 0., // 16 % 1., // 17 % 0., // 18 % 1., // 19 % 0., // 20 % 1., // 21 % 0., // 22 % 1., // 23 % 0., // 24 % 1., // 25 % 0., // 26 % 1., // 27 % 0., // 28 % 1., // 29 % 0., // 30 % 1., // 31 % 0., // 32 % 1., // 33 % 0., // 34 % 1., // 35 % 0., // 36 % 1., // 37 % 0., // 38 % 1., // 39 % 0., // 40 % 1., // 41 % 0., // 42 % 1., // 43 % 0., // 44 % 1., // 45 % 0., // 46 % 1., // 47 % 0., // 48 % 1., // 49 % 0., // 50 % 1., // 51 % 0., // 52 % 1., // 53 % 0., // 54 % 1., // 55 % 0., // 56 % 1., // 57 % 0., // 58 % 1., // 59 % 0., // 60 % 1., // 61 % 0., // 62 % 1., // 63 % 0., // 64 % 1., // 65 % 0., // 66 % 1., // 67 % 0., // 68 % 1., // 69 % 0., // 70 % 1., // 71 % 0., // 72 % 1., // 73 % 0., // 74 % 1., // 75 % 0., // 76 % 1., // 77 % 0., // 78 % 1., // 79 % 0., // 80 % 1., // 81 % 0., // 82 % ], % [ // 3 % 3.232777164053174, // 1 % -1.798002893065565, // 2 % 3.232777164053174, // 3 % -1.798002893065565, // 4 % 3.232777164053174, // 5 % -1.798002893065565, // 6 % 3.232777164053174, // 7 % -1.798002893065565, // 8 % 3.232777164053174, // 9 % -1.798002893065565, // 10 % 3.232777164053174, // 11 % -1.798002893065565, // 12 % 3.232777164053174, // 13 % -1.798002893065565, // 14 % 3.232777164053174, // 15 % -1.798002893065565, // 16 % 3.232777164053174, // 17 % -1.798002893065565, // 18 % 3.232777164053174, // 19 % -1.798002893065565, // 20 % 3.232777164053174, // 21 % -1.798002893065565, // 22 % 3.232777164053174, // 23 % -1.798002893065565, // 24 % 3.232777164053174, // 25 % -1.798002893065565, // 26 % 3.232777164053174, // 27 % -1.798002893065565, // 28 % 3.232777164053174, // 29 % -1.798002893065565, // 30 % 3.232777164053174, // 31 % -1.798002893065565, // 32 % 3.232777164053174, // 33 % -1.798002893065565, // 34 % 3.232777164053174, // 35 % -1.798002893065565, // 36 % 3.00145271296859, // 37 % -0.1986685953770433, // 38 % 1.732050807568877, // 39 % -1.198668595377044, // 40 % 1.500726356484295, // 41 % 0.4006657023114784, // 42 % 0.2313244510845824, // 43 % -0.5993342976885219, // 44 % -1.269401905399713, // 45 % 0., // 46 % -1.269401905399713, // 47 % 0., // 48 % -1.269401905399713, // 49 % 0., // 50 % -1.269401905399713, // 51 % 0., // 52 % -1.269401905399713, // 53 % 0., // 54 % -1.269401905399713, // 55 % 0., // 56 % -1.269401905399713, // 57 % 0., // 58 % -1.269401905399713, // 59 % 0., // 60 % -1.269401905399713, // 61 % 0., // 62 % -1.269401905399713, // 63 % 0., // 64 % -1.269401905399713, // 65 % 0., // 66 % -1.269401905399713, // 67 % 0., // 68 % -1.269401905399713, // 69 % 0., // 70 % -1.269401905399713, // 71 % 0., // 72 % -1.269401905399713, // 73 % 0., // 74 % -1.269401905399713, // 75 % 0., // 76 % -1.269401905399713, // 77 % 0., // 78 % -1.269401905399713, // 79 % 0., // 80 % 0., // 81 % 1., // 82 % ], % ]; %Vergleichsrichtung=[[1,0,0],[2,1,0]]; %Nenner=11552; %DD=[ % [72,37], % [80,80], % [81,81], % [82,82], % ]; % %Beweglichkeitsgrad=1; %Einsetzkantenzahl=2; %Maxi=22; Maxj=1; MaxInvAij=1074519.176295355; //=Kante [ 7, 12 ] %gerechnet_mit_Button="acos(1/4)"; % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/14.14/6.01, 2/13.40/7.87, 3/12.16/6.30, 4/11.42/8.15, 5/12.66/9.73, 6/10.18/6.58, 7/10.40/4.60, 8/11.95/3.33, 9/12.27/5.30, 10/13.82/4.04, 11/13.50/2.06, 12/8.57/5.40, 13/10.07/0.00, 14/11.79/1.03, 15/10.04/2.00, 16/11.75/3.03, 17/10.00/4.00, 18/8.07/3.46, 19/9.07/1.73, 20/8.07/0.00, 21/7.07/1.73, 22/6.07/0.00, 23/0.00/6.01, 24/0.74/7.87, 25/1.98/6.30, 26/2.72/8.15, 27/1.48/9.73, 28/3.96/6.58, 29/3.74/4.60, 30/2.19/3.33, 31/1.87/5.30, 32/0.32/4.04, 33/0.64/2.06, 34/5.57/5.40, 35/4.07/0.00, 36/2.36/1.03, 37/4.11/2.00, 38/2.39/3.03, 39/4.14/4.00, 40/6.07/3.46, 41/5.07/1.73} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-1) -- (p-9); \draw[line width=2,blue!50] (p-1) -- (p-10); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-6) -- (p-3); \draw[line width=2,blue!50] (p-6) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-11) -- (p-8); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-11) -- (p-14); \draw[line width=2,blue!50] (p-11) -- (p-16); \draw[line width=2,blue!50] (p-12) -- (p-7); \draw[line width=2,blue!50] (p-12) -- (p-6); \draw[line width=2,blue!50] (p-12) -- (p-17); \draw[line width=2,blue!50] (p-12) -- (p-18); \draw[line width=2,blue!50] (p-13) -- (p-19); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-17) -- (p-18); \draw[line width=2,blue!50] (p-19) -- (p-18); \draw[line width=2,orange!50] (p-23) -- (p-31); \draw[line width=2,orange!50] (p-23) -- (p-32); \draw[line width=2,orange!50] (p-25) -- (p-23); \draw[line width=2,orange!50] (p-28) -- (p-25); \draw[line width=2,orange!50] (p-28) -- (p-29); \draw[line width=2,orange!50] (p-30) -- (p-29); \draw[line width=2,orange!50] (p-31) -- (p-29); \draw[line width=2,orange!50] (p-33) -- (p-30); \draw[line width=2,orange!50] (p-33) -- (p-32); \draw[line width=2,orange!50] (p-33) -- (p-36); \draw[line width=2,orange!50] (p-33) -- (p-38); \draw[line width=2,orange!50] (p-34) -- (p-28); \draw[line width=2,orange!50] (p-34) -- (p-29); \draw[line width=2,orange!50] (p-34) -- (p-39); \draw[line width=2,orange!50] (p-34) -- (p-40); \draw[line width=2,orange!50] (p-35) -- (p-41); \draw[line width=2,orange!50] (p-36) -- (p-35); \draw[line width=2,orange!50] (p-37) -- (p-35); \draw[line width=2,orange!50] (p-39) -- (p-37); \draw[line width=2,orange!50] (p-39) -- (p-38); \draw[line width=2,orange!50] (p-39) -- (p-40); \draw[line width=2,orange!50] (p-41) -- (p-40); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 1/9, 1/10, 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 6/7, 8/7, 9/7, 9/8, 10/8, 10/9, 11/8, 11/10, 11/14, 11/16, 12/7, 12/6, 12/17, 12/18, 13/19, 13/20, 14/13, 15/13, 15/14, 16/14, 16/15, 17/15, 17/16, 17/18, 18/40, 19/18, 20/19, 21/20, 21/19, 21/41, 22/20, 22/21, 22/41, 23/31, 23/32, 24/23, 25/23, 25/24, 26/24, 26/25, 27/24, 27/26, 28/25, 28/26, 28/29, 30/29, 31/29, 31/30, 32/30, 32/31, 33/30, 33/32, 33/36, 33/38, 34/28, 34/29, 34/39, 34/40, 35/41, 35/22, 36/35, 37/35, 37/36, 38/36, 38/37, 39/37, 39/38, 39/40, 41/40} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/322, 2/82, 3/262, 4/82, 5/82, 6/66, 7/306, 8/171, 9/111, 10/351, 11/1, 12/186, 13/241, 14/301, 15/181, 16/1, 17/346, 18/226, 19/90, 20/330, 21/90, 22/210, 23/218, 24/218, 25/338, 26/98, 27/98, 28/338, 29/234, 30/9, 31/69, 32/249, 33/179, 34/354, 35/299, 36/239, 37/299, 38/59, 39/194, 40/314, 41/90} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Er enthält 2 Bereiche für Einsetzkanten, orange und hellblau markiert, in der Mitte in Richtung P41-P19 besteht eine Beweglichkeit mit Beweglichkeitsspielraum 0. Der Abzählreim Einsetzkanten=Beweglichkeit+1 ist erfüllt. Die Beweglichkeit würde sich so bemerkbar machen: Wenn man den linken Teilgraph orange festhält und versucht, den rechten Teilgraph vertikal zu verschieben, trifft man nicht auf so festen Widerstand wie bei einem starren Graph zu erwarten wäre, weil die Punkte P41 und P19 aus ihrer Position gedrückt werden. Das soll eine Rechtfertigung sein, das auch als beweglich und Kante P21-P13 als Anfügekante einzustufen. \quoteon(2022-04-25 06:29 - haribo in Beitrag No. 2313) Slash, Anstelle punktsymetrie die gespiegelt Variante verbessert es einiges, bringt beide Dreier in Nähe zueinander , im Sinne des Fortschritts... https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_3C175A65-6117-4974-BCC1-70BCC88D2849.jpeg Im Sinne von Stefans Argumentation ist aber wohl der untere rechte kite so aufgebrochen dass ihm seine einsetzkante fehlt, ? Dann kann das scheints nix werden??? \quoteoff Die richtige Antwort muss lauten, nur Kante P32-P33 ist eine Einsetzkante und sollte drinbleiben wenn man die Einsetzkanteneigenschaft erhalten will. Die andere Kante P32-P40 ist nach neuester Betrachtungsweise eine Anfügekante. Hierbei habe ich einen Programmfehler bemerkt. Button "beweglich?" sagt 1-fach beweglich, aber anschließendes "extrapolieren" findet die Bewegung nicht. Ich nehme an, beim Versuch, P32 nach rechts zu bewegen, kann sich P39 nicht entscheiden, ob nach links oder rechts zu gehen. 48 Knoten, 4×Grad 2, 1×Grad 3, 42×Grad 4, 1×Grad 9, 0 Überschneidungen, 94 Kanten, minimal 0.99999999999999589217, maximal 1.00000000000000355271, Einsetzkanten=Beweglichkeit+1, $ %Eingabe war: % %#2324-4 % % %P[1]=[16.06089843006874,10.083151692804961]; P[2]=[65.25118552852388,-1.6266286284290459]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); A(11,12,ab(5,12,[1,12])); A(12,22,ab(12,5,[1,10])); A(12,5,ab(5,12,[1,12])); N(42,29,12); Z(32,33); Z(32,40); N(43,42,33); N(44,32,40); L(45,42,43); N(46,31,45); L(47,45,43); N(48,47,32); % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.86/0.93, 2/4.80/0.46, 3/4.23/2.38, 4/6.18/1.92, 5/6.75/0.00, 6/5.60/3.83, 7/3.85/4.80, 8/1.93/4.26, 9/3.35/2.86, 10/1.43/2.33, 11/0.00/3.73, 12/5.57/5.83, 13/0.29/7.72, 14/0.14/5.72, 15/1.94/6.59, 16/1.80/4.60, 17/3.60/5.47, 18/4.27/7.36, 19/3.43/9.17, 20/2.28/7.54, 21/1.44/9.35, 22/2.59/10.99, 23/6.57/11.35, 24/4.58/11.17, 25/5.73/9.53, 26/3.74/9.35, 27/4.89/7.72, 28/6.86/7.36, 29/8.517/8.478, 30/6.72/9.35, 31/8.37/10.47, 32/9.46/4.91, 33/7.51/5.37, 34/8.08/3.45, 35/6.14/3.92, 36/6.71/2.00, 37/8.46/1.03, 38/10.39/1.57, 39/8.96/2.97, 40/10.89/3.51, 41/12.31/2.11, 42/7.22/6.95, 43/9.17/6.49, 44/11.38/5.44, 45/8.596/8.408, 46/10.18/9.62, 47/10.54/7.94, 48/11.11/6.03} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 1/9, 1/10, 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 5/36, 5/37, 6/3, 6/4, 6/7, 8/7, 9/7, 9/8, 10/8, 10/9, 11/8, 11/10, 11/14, 11/16, 12/7, 12/6, 12/17, 12/18, 12/27, 12/28, 12/33, 12/35, 13/20, 13/21, 14/13, 15/13, 15/14, 16/14, 16/15, 17/15, 17/16, 17/18, 19/18, 20/18, 20/19, 21/19, 21/20, 22/19, 22/21, 22/24, 22/26, 23/30, 23/31, 24/23, 25/23, 25/24, 26/24, 26/25, 27/25, 27/26, 27/28, 29/28, 30/28, 30/29, 31/29, 31/30, 32/39, 34/32, 34/33, 35/33, 35/34, 36/34, 36/35, 36/37, 38/37, 39/37, 39/38, 40/38, 40/39, 41/38, 41/40, 42/29, 42/12, 43/42, 43/33, 44/32, 44/40, 45/42, 45/43, 46/31, 46/45, 47/45, 47/43, 48/47, 48/32} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 32/138, 33/77, 39/106, 40/106} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Auch in Graph #2362 ist nach der neuen Betrachtung P89-P67 eine Anfügekante, dafür wird aber mit P81-P82 eine Einsetzkante entfernt, welche am Schluss dann als nicht einstellbaŕe Kante übrigbleibt. Soweit die Stellen, wo ich das wegen der nur 22 Einsetzkanten des Doppelkite korrigieren muss. \quoteon(2022-05-02 06:03 - haribo in Beitrag No. 2340) @stefan, du schreibst in #2325: Es besteht aber die Möglichkeit, die beiden 2er-Knoten mit einer Krebsschere (zwei Doppelkites) zu verbinden und die bringt die beiden fehlenden Einsetzkanten mit. Falls der Abstand der beiden 2er-Knoten exakt gleich der Länge eines Doppelkites wäre, reicht auch ein Doppelkite Ich glaub ein genau passender doppelkite könnte sogar 4 Einsetzkanten generieren, Das ist doch wohl beim 4/8er der Fall? Der benötigt doch gemäß deinen Ausführungen 7 Einsetzkanten, 3 befinden sich in den vier Kits welche den 8ee Knoten bilden, dessen beide 2er Knoten werden vom exakt passenden doppelkite gebunden, damit müssen die vier fehlenden Einsetzkanten ja dann wohl alle 4 in diesem doppelkite liegen? EDIT“er braucht nur 5, also fehlen nur zwei und die können sowohl im genau eingepasstem doppelkite oder in den dazugehörigen (zum genau einpassen dazugehörig)Flügelspitzen liegen Eine ist sowieso im zweiten kite des doppelkites, durch die genaue einpassung ist auch im ersten kite eine einsetzkante, fehlen immer noch zwei... EDIT nein die fehlen eben nicht \quoteoff So ist es. \quoteon(2022-05-02 11:51 - haribo in Beitrag No. 2341) habs jetztbeim 120er selbst untersucht, er scheint auch 4 einsatzkanten zu haben, drei davon, könnte man sagen, liegen sozusagen im letzten (12.) element, der ring muss aber noch geschlossen sein, und es dürfen wieder nicht alle drei vom gleichen knoten abgehen (da sonst der vierte an diesen knoten anschliessende beweglich würde) die vierte einsatzkante kann scheints irgendwo anders liegen, aufgrund der symetrie kann das 12. element natürlich jedes sein \quoteoff Bei den Ringgraphen kenne ich noch keine Methode, die Einsetzkanten durch bloßes Draufschauen auseinanderzusortieren. Die Bereiche überlappen sich und jede Kante ist eine Einsetzkante. Ich habe am Beispiel des 120er versucht, mit exakter Berechnung mit Button "acos(1/4)" die Bereiche zu lokalisieren, doch ein bestimmtes System habe ich darin nicht erkannt. Möglicherweise kann man eine 30°-Drehung eines Bereiches durch eine geschickte Überlagerung mehrerer der 4 Bereiche erzeugen, als additive Überlagerung verschiedener Spannungszustände. Ausgangsgraph: 60 Knoten, 60×Grad 4, 0 Überschneidungen, 120 Kanten, minimal 0.99999999999999156231, maximal 1.00000000000000288658, Einsetzkanten=Beweglichkeit+3, $ %Eingabe war: % %Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2); N(46,6,3); N(47,10,8); N(48,14,12); N(49,18,16); N(50,22,20); N(51,26,24); N(52,30,28); N(53,34,32); N(54,38,36); N(55,42,40); N(56,46,4); N(57,56,5); L(58,57,5); L(59,57,58); N(60,44,55); A(58,45,Bew(5)); A(45,59,Bew(6)); A(59,60,Bew(6)); A(46,47,Bew(6)); A(47,48,Bew(6)); A(48,49,Bew(6)); A(49,50,Bew(6)); A(50,51,Bew(6)); A(51,52,Bew(6)); A(52,53,Bew(6)); A(53,54,Bew(6)); A(54,55,Bew(6)); A(60,56,Bew(6)); W(); % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/6.60, 29/4.73/7.46, 30/4.73/6.46, 31/5.60/6.96, 32/5.60/5.96, 33/6.46/6.46, 34/5.96/5.60, 35/6.96/5.60, 36/6.46/4.73, 37/7.46/4.73, 38/6.60/4.23, 39/7.46/3.73, 40/6.60/3.23, 41/7.46/2.73, 42/6.46/2.73, 43/6.96/1.87, 44/5.96/1.87, 45/6.46/1.00, 46/3.23/1.87, 47/2.37/2.37, 48/1.87/3.23, 49/1.87/4.23, 50/2.37/5.10, 51/3.23/5.60, 52/4.23/5.60, 53/5.10/5.10, 54/5.60/4.23, 55/5.60/3.23, 56/4.23/1.87, 57/4.73/1.00, 58/5.60/0.50, 59/5.60/1.50, 60/5.10/2.37} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 15/13, 15/14, 16/15, 16/14, 17/15, 17/16, 18/17, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 27/25, 27/26, 28/27, 28/26, 29/27, 29/28, 30/29, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/33, 35/33, 35/34, 36/35, 36/34, 37/35, 37/36, 38/37, 39/37, 39/38, 40/39, 40/38, 41/39, 41/40, 42/41, 43/41, 43/42, 44/43, 44/42, 45/43, 45/44, 45/59, 46/6, 46/3, 46/47, 47/10, 47/8, 47/48, 48/14, 48/12, 48/49, 49/18, 49/16, 49/50, 50/22, 50/20, 50/51, 51/26, 51/24, 51/52, 52/30, 52/28, 52/53, 53/34, 53/32, 53/54, 54/38, 54/36, 54/55, 55/42, 55/40, 56/46, 56/4, 57/56, 57/5, 58/57, 58/5, 58/45, 59/57, 59/58, 59/60, 60/44, 60/55, 60/56} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,60} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/180, 8/60, 9/180, 10/30, 11/150, 12/90, 13/240, 14/300, 15/120, 16/60, 17/120, 18/330, 19/150, 20/330, 21/180, 22/240, 23/60, 24/300, 25/150, 26/210, 27/30, 28/270, 29/30, 30/180, 31/60, 32/240, 33/360, 34/150, 35/330, 36/270, 37/60, 38/180, 39/360, 40/240, 41/300, 42/150, 43/330, 44/150, 45/270, 46/18, 47/348, 48/78, 49/48, 50/257, 51/347, 52/197, 53/167, 54/257, 55/228, 56/167, 57/120, 58/360, 59/120, 60/198} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Bereich 1 (hellblau): $ %Eingabe war: % %Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2); N(46,6,3); N(47,10,8); N(48,14,12); N(49,18,16); N(50,22,20); N(51,26,24); N(52,30,28); N(53,34,32); N(54,38,36); N(55,42,40); N(56,46,4); N(57,56,5); L(58,57,5); L(59,57,58); N(60,44,55); A(58,45,Bew(5)); A(45,59,Bew(6)); A(59,60,Bew(6)); A(46,47,Bew(6)); A(47,48,Bew(6)); A(48,49,Bew(6)); A(49,50,Bew(6)); A(50,51,Bew(6)); A(51,52,Bew(6)); A(52,53,Bew(6)); A(53,54,Bew(6)); A(54,55,Bew(6)); A(60,56,Bew(6)); W(); % % % % % %Belastungsarray=[ % [ // 0 % 1.732050807568877, // 1 (P1-P2) % -1.732050807568877, // 2 (P1-P3) % -0.5773502691896255, // 3 (P2-P3) % -0.5773502691896255, // 4 (P3-P4) % 0.5773502691896255, // 5 (P2-P4) % -0.5773502691896255, // 6 (P4-P5) % 1.154700538379251, // 7 (P2-P5) % 1., // 8 (P1-P6) % 1., // 9 (P1-P7) % 1., // 10 (P6-P7) % -1., // 11 (P7-P8) % 0., // 12 (P6-P8) % 2., // 13 (P7-P9) % -1., // 14 (P8-P9) % 0., // 15 (P9-P10) % 1.732050807568877, // 16 (P9-P11) % 1.154700538379251, // 17 (P10-P11) % -1.154700538379251, // 18 (P11-P12) % -0.5773502691896255, // 19 (P10-P12) % 2.886751345948127, // 20 (P11-P13) % -2.309401076758502, // 21 (P12-P13) % 1., // 22 (P13-P14) % 2., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 0., // 26 (P14-P16) % 3., // 27 (P15-P17) % -1., // 28 (P16-P17) % -0.5773502691896255, // 29 (P17-P18) % 2.886751345948127, // 30 (P17-P19) % 0.5773502691896255, // 31 (P18-P19) % -0.5773502691896255, // 32 (P19-P20) % -0.5773502691896255, // 33 (P18-P20) % 3.464101615137753, // 34 (P19-P21) % -1.732050807568877, // 35 (P20-P21) % 0., // 36 (P21-P22) % 3., // 37 (P21-P23) % 0., // 38 (P22-P23) % 0., // 39 (P23-P24) % 0., // 40 (P22-P24) % 3., // 41 (P23-P25) % 0., // 42 (P24-P25) % -1.732050807568877, // 43 (P25-P26) % 3.464101615137753, // 44 (P25-P27) % -0.5773502691896255, // 45 (P26-P27) % 0.5773502691896255, // 46 (P27-P28) % -0.5773502691896255, // 47 (P26-P28) % 2.886751345948127, // 48 (P27-P29) % -0.5773502691896255, // 49 (P28-P29) % -1., // 50 (P29-P30) % 3., // 51 (P29-P31) % -1., // 52 (P30-P31) % 1., // 53 (P31-P32) % 0., // 54 (P30-P32) % 2., // 55 (P31-P33) % 1., // 56 (P32-P33) % -2.309401076758502, // 57 (P33-P34) % 2.886751345948127, // 58 (P33-P35) % -1.154700538379251, // 59 (P34-P35) % 1.154700538379251, // 60 (P35-P36) % -0.5773502691896255, // 61 (P34-P36) % 1.732050807568877, // 62 (P35-P37) % 0., // 63 (P36-P37) % -1., // 64 (P37-P38) % 2., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 0., // 68 (P38-P40) % 1., // 69 (P39-P41) % 1., // 70 (P40-P41) % -1.732050807568877, // 71 (P41-P42) % 1.732050807568877, // 72 (P41-P43) % -0.5773502691896255, // 73 (P42-P43) % 0.5773502691896255, // 74 (P43-P44) % -0.5773502691896255, // 75 (P42-P44) % 1.154700538379251, // 76 (P43-P45) % -0.5773502691896255, // 77 (P44-P45) % 0., // 78 (P45-P59) % 1.732050807568877, // 79 (P6-P46) % -2., // 80 (P3-P46) % -1., // 81 (P46-P47) % 1., // 82 (P10-P47) % -1.732050807568877, // 83 (P8-P47) % -1.732050807568877, // 84 (P47-P48) % 1.732050807568877, // 85 (P14-P48) % -3., // 86 (P12-P48) % -3., // 87 (P48-P49) % 0., // 88 (P18-P49) % -1.732050807568877, // 89 (P16-P49) % -3.464101615137753, // 90 (P49-P50) % 0., // 91 (P22-P50) % -2., // 92 (P20-P50) % -4., // 93 (P50-P51) % -2., // 94 (P26-P51) % 0., // 95 (P24-P51) % -3.464101615137753, // 96 (P51-P52) % -1.732050807568877, // 97 (P30-P52) % 0., // 98 (P28-P52) % -3., // 99 (P52-P53) % -3., // 100 (P34-P53) % 1.732050807568877, // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % -1.732050807568877, // 103 (P38-P54) % 1., // 104 (P36-P54) % -1., // 105 (P54-P55) % -2., // 106 (P42-P55) % 1.732050807568877, // 107 (P40-P55) % 0., // 108 (P46-P56) % 0., // 109 (P4-P56) % 0., // 110 (P56-P57) % 0., // 111 (P5-P57) % 0., // 112 (P57-P58) % 1., // 113 (P5-P58) % 1., // 114 (P45-P58) % 0., // 115 (P57-P59) % 0., // 116 (P58-P59) % 0., // 117 (P59-P60) % 0., // 118 (P44-P60) % 0., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 1 % 0., // 1 (P1-P2) % -1.732050807568877, // 2 (P1-P3) % 0.5773502691896255, // 3 (P2-P3) % -1.154700538379251, // 4 (P3-P4) % -0.5773502691896255, // 5 (P2-P4) % -2.886751345948127, // 6 (P4-P5) % 0.5773502691896255, // 7 (P2-P5) % 2., // 8 (P1-P6) % -1., // 9 (P1-P7) % 0., // 10 (P6-P7) % 0., // 11 (P7-P8) % 1., // 12 (P6-P8) % -1., // 13 (P7-P9) % 2., // 14 (P8-P9) % -1.732050807568877, // 15 (P9-P10) % 0., // 16 (P9-P11) % 0.5773502691896255, // 17 (P10-P11) % -0.5773502691896255, // 18 (P11-P12) % -1.154700538379251, // 19 (P10-P12) % 0.5773502691896255, // 20 (P11-P13) % -2.886751345948127, // 21 (P12-P13) % 3., // 22 (P13-P14) % -1., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 1., // 26 (P14-P16) % 0., // 27 (P15-P17) % 1., // 28 (P16-P17) % -1.154700538379251, // 29 (P17-P18) % 0.5773502691896255, // 30 (P17-P19) % 1.154700538379251, // 31 (P18-P19) % -1.154700538379251, // 32 (P19-P20) % -1.154700538379251, // 33 (P18-P20) % 1.732050807568877, // 34 (P19-P21) % -3.464101615137753, // 35 (P20-P21) % 3., // 36 (P21-P22) % 0., // 37 (P21-P23) % 1., // 38 (P22-P23) % -1., // 39 (P23-P24) % 1., // 40 (P22-P24) % 1., // 41 (P23-P25) % 1., // 42 (P24-P25) % -1.732050807568877, // 43 (P25-P26) % 1.732050807568877, // 44 (P25-P27) % 0.5773502691896255, // 45 (P26-P27) % -0.5773502691896255, // 46 (P27-P28) % -1.154700538379251, // 47 (P26-P28) % 2.309401076758502, // 48 (P27-P29) % -2.886751345948127, // 49 (P28-P29) % 2., // 50 (P29-P30) % 1., // 51 (P29-P31) % 0., // 52 (P30-P31) % 0., // 53 (P31-P32) % 1., // 54 (P30-P32) % 1., // 55 (P31-P33) % 2., // 56 (P32-P33) % -2.886751345948127, // 57 (P33-P34) % 2.309401076758502, // 58 (P33-P35) % -0.5773502691896255, // 59 (P34-P35) % 0.5773502691896255, // 60 (P35-P36) % -1.154700538379251, // 61 (P34-P36) % 1.732050807568877, // 62 (P35-P37) % -1.732050807568877, // 63 (P36-P37) % 1., // 64 (P37-P38) % 1., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 1., // 68 (P38-P40) % 0., // 69 (P39-P41) % 3., // 70 (P40-P41) % -3.464101615137753, // 71 (P41-P42) % 1.732050807568877, // 72 (P41-P43) % -1.154700538379251, // 73 (P42-P43) % 1.154700538379251, // 74 (P43-P44) % -1.154700538379251, // 75 (P42-P44) % 0.5773502691896255, // 76 (P43-P45) % -1.154700538379251, // 77 (P44-P45) % 1., // 78 (P45-P59) % 1.732050807568877, // 79 (P6-P46) % -1., // 80 (P3-P46) % 1., // 81 (P46-P47) % -1., // 82 (P10-P47) % 1.732050807568877, // 83 (P8-P47) % 1.732050807568877, // 84 (P47-P48) % 3.464101615137753, // 85 (P14-P48) % -3., // 86 (P12-P48) % 0., // 87 (P48-P49) % 0., // 88 (P18-P49) % 0., // 89 (P16-P49) % 0., // 90 (P49-P50) % 3.464101615137753, // 91 (P22-P50) % -4., // 92 (P20-P50) % -2., // 93 (P50-P51) % -1., // 94 (P26-P51) % 0., // 95 (P24-P51) % -1.732050807568877, // 96 (P51-P52) % 1.732050807568877, // 97 (P30-P52) % -3., // 98 (P28-P52) % -3., // 99 (P52-P53) % -3., // 100 (P34-P53) % 1.732050807568877, // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % 0., // 103 (P38-P54) % -1., // 104 (P36-P54) % -2., // 105 (P54-P55) % -4., // 106 (P42-P55) % 3.464101615137753, // 107 (P40-P55) % 1.732050807568877, // 108 (P46-P56) % -3., // 109 (P4-P56) % 3.464101615137753, // 110 (P56-P57) % 3., // 111 (P5-P57) % 1., // 112 (P57-P58) % -1., // 113 (P5-P58) % 0., // 114 (P45-P58) % 1., // 115 (P57-P59) % -1., // 116 (P58-P59) % 0., // 117 (P59-P60) % 0., // 118 (P44-P60) % 0., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 2 % 2., // 1 (P1-P2) % -2., // 2 (P1-P3) % -1.333333333333333, // 3 (P2-P3) % -0.3333333333333333, // 4 (P3-P4) % 1.333333333333333, // 5 (P2-P4) % 0.6666666666666666, // 6 (P4-P5) % 0.6666666666666666, // 7 (P2-P5) % 1.154700538379251, // 8 (P1-P6) % 1.154700538379251, // 9 (P1-P7) % 1.154700538379251, // 10 (P6-P7) % -1.154700538379251, // 11 (P7-P8) % 0., // 12 (P6-P8) % 2.309401076758502, // 13 (P7-P9) % -1.154700538379251, // 14 (P8-P9) % 0., // 15 (P9-P10) % 2., // 16 (P9-P11) % 0.6666666666666666, // 17 (P10-P11) % -0.6666666666666666, // 18 (P11-P12) % -0.3333333333333333, // 19 (P10-P12) % 2.666666666666667, // 20 (P11-P13) % -1.333333333333333, // 21 (P12-P13) % 0., // 22 (P13-P14) % 2.309401076758502, // 23 (P13-P15) % 0., // 24 (P14-P15) % 0., // 25 (P15-P16) % 0., // 26 (P14-P16) % 2.309401076758502, // 27 (P15-P17) % 0., // 28 (P16-P17) % -1.333333333333333, // 29 (P17-P18) % 2.666666666666667, // 30 (P17-P19) % -0.6666666666666666, // 31 (P18-P19) % 0.6666666666666666, // 32 (P19-P20) % -0.3333333333333333, // 33 (P18-P20) % 2., // 34 (P19-P21) % 0., // 35 (P20-P21) % -1.154700538379251, // 36 (P21-P22) % 2.309401076758502, // 37 (P21-P23) % -1.154700538379251, // 38 (P22-P23) % 1.154700538379251, // 39 (P23-P24) % 0., // 40 (P22-P24) % 1.154700538379251, // 41 (P23-P25) % 1.154700538379251, // 42 (P24-P25) % -2., // 43 (P25-P26) % 2., // 44 (P25-P27) % -1.333333333333333, // 45 (P26-P27) % 1.333333333333333, // 46 (P27-P28) % -0.3333333333333333, // 47 (P26-P28) % 0.6666666666666666, // 48 (P27-P29) % 0.6666666666666666, // 49 (P28-P29) % -1.154700538379251, // 50 (P29-P30) % 1.154700538379251, // 51 (P29-P31) % -1.154700538379251, // 52 (P30-P31) % 1.154700538379251, // 53 (P31-P32) % 0., // 54 (P30-P32) % 0., // 55 (P31-P33) % 1.154700538379251, // 56 (P32-P33) % -1.333333333333333, // 57 (P33-P34) % 0.6666666666666666, // 58 (P33-P35) % -0.6666666666666666, // 59 (P34-P35) % 0.6666666666666666, // 60 (P35-P36) % -0.3333333333333333, // 61 (P34-P36) % 0., // 62 (P35-P37) % 0., // 63 (P36-P37) % 0., // 64 (P37-P38) % 0., // 65 (P37-P39) % 0., // 66 (P38-P39) % 0., // 67 (P39-P40) % 0., // 68 (P38-P40) % 0., // 69 (P39-P41) % 0., // 70 (P40-P41) % 0., // 71 (P41-P42) % 0., // 72 (P41-P43) % 0.6666666666666666, // 73 (P42-P43) % -0.6666666666666666, // 74 (P43-P44) % -0.3333333333333333, // 75 (P42-P44) % 0.6666666666666666, // 76 (P43-P45) % -1.333333333333333, // 77 (P44-P45) % 1.154700538379251, // 78 (P45-P59) % 2., // 79 (P6-P46) % -2.886751345948127, // 80 (P3-P46) % -2.309401076758502, // 81 (P46-P47) % 0.5773502691896255, // 82 (P10-P47) % -2., // 83 (P8-P47) % -3., // 84 (P47-P48) % 0., // 85 (P14-P48) % -1.732050807568877, // 86 (P12-P48) % -3.464101615137753, // 87 (P48-P49) % -1.732050807568877, // 88 (P18-P49) % 0., // 89 (P16-P49) % -3., // 90 (P49-P50) % -2., // 91 (P22-P50) % 0.5773502691896255, // 92 (P20-P50) % -2.309401076758502, // 93 (P50-P51) % -2.886751345948127, // 94 (P26-P51) % 2., // 95 (P24-P51) % -1., // 96 (P51-P52) % -2., // 97 (P30-P52) % 1.732050807568877, // 98 (P28-P52) % 0., // 99 (P52-P53) % -1.732050807568877, // 100 (P34-P53) % 2., // 101 (P32-P53) % 1., // 102 (P53-P54) % 0., // 103 (P38-P54) % 0.5773502691896255, // 104 (P36-P54) % 1.154700538379251, // 105 (P54-P55) % 0.5773502691896255, // 106 (P42-P55) % 0., // 107 (P40-P55) % -1., // 108 (P46-P56) % 1.732050807568877, // 109 (P4-P56) % -2., // 110 (P56-P57) % -1.154700538379251, // 111 (P5-P57) % -1.154700538379251, // 112 (P57-P58) % 1.154700538379251, // 113 (P5-P58) % 0., // 114 (P45-P58) % 0., // 115 (P57-P59) % 1.154700538379251, // 116 (P58-P59) % 2., // 117 (P59-P60) % -1.732050807568877, // 118 (P44-P60) % 1., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 3 % -1.154700538379251, // 1 (P1-P2) % 0.5773502691896255, // 2 (P1-P3) % 0.5773502691896255, // 3 (P2-P3) % 0., // 4 (P3-P4) % -0.5773502691896255, // 5 (P2-P4) % -0.5773502691896255, // 6 (P4-P5) % -0.5773502691896255, // 7 (P2-P5) % 0., // 8 (P1-P6) % -1., // 9 (P1-P7) % 0., // 10 (P6-P7) % 0., // 11 (P7-P8) % 0., // 12 (P6-P8) % -1., // 13 (P7-P9) % 0., // 14 (P8-P9) % 0.5773502691896255, // 15 (P9-P10) % -1.154700538379251, // 16 (P9-P11) % 0.5773502691896255, // 17 (P10-P11) % -0.5773502691896255, // 18 (P11-P12) % 0., // 19 (P10-P12) % -0.5773502691896255, // 20 (P11-P13) % -0.5773502691896255, // 21 (P12-P13) % 1., // 22 (P13-P14) % -1., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 0., // 26 (P14-P16) % 0., // 27 (P15-P17) % -1., // 28 (P16-P17) % 1.154700538379251, // 29 (P17-P18) % -0.5773502691896255, // 30 (P17-P19) % 1.154700538379251, // 31 (P18-P19) % -1.154700538379251, // 32 (P19-P20) % 0., // 33 (P18-P20) % 0.5773502691896255, // 34 (P19-P21) % -1.154700538379251, // 35 (P20-P21) % 1., // 36 (P21-P22) % 0., // 37 (P21-P23) % 1., // 38 (P22-P23) % -1., // 39 (P23-P24) % 0., // 40 (P22-P24) % 1., // 41 (P23-P25) % -1., // 42 (P24-P25) % 0.5773502691896255, // 43 (P25-P26) % 0.5773502691896255, // 44 (P25-P27) % 0.5773502691896255, // 45 (P26-P27) % -0.5773502691896255, // 46 (P27-P28) % 0., // 47 (P26-P28) % 1.154700538379251, // 48 (P27-P29) % -0.5773502691896255, // 49 (P28-P29) % 0., // 50 (P29-P30) % 1., // 51 (P29-P31) % 0., // 52 (P30-P31) % 0., // 53 (P31-P32) % 0., // 54 (P30-P32) % 1., // 55 (P31-P33) % 0., // 56 (P32-P33) % -0.5773502691896255, // 57 (P33-P34) % 1.154700538379251, // 58 (P33-P35) % -0.5773502691896255, // 59 (P34-P35) % 0.5773502691896255, // 60 (P35-P36) % 0., // 61 (P34-P36) % 0.5773502691896255, // 62 (P35-P37) % 0.5773502691896255, // 63 (P36-P37) % -1., // 64 (P37-P38) % 1., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 0., // 68 (P38-P40) % 0., // 69 (P39-P41) % 1., // 70 (P40-P41) % -1.154700538379251, // 71 (P41-P42) % 0.5773502691896255, // 72 (P41-P43) % -1.154700538379251, // 73 (P42-P43) % 1.154700538379251, // 74 (P43-P44) % 0., // 75 (P42-P44) % -0.5773502691896255, // 76 (P43-P45) % 1.154700538379251, // 77 (P44-P45) % -1., // 78 (P45-P59) % 0., // 79 (P6-P46) % 1., // 80 (P3-P46) % 2., // 81 (P46-P47) % 1., // 82 (P10-P47) % 0., // 83 (P8-P47) % 1.732050807568877, // 84 (P47-P48) % 1.732050807568877, // 85 (P14-P48) % -1., // 86 (P12-P48) % 1., // 87 (P48-P49) % 2., // 88 (P18-P49) % -1.732050807568877, // 89 (P16-P49) % 0., // 90 (P49-P50) % 1.732050807568877, // 91 (P22-P50) % -2., // 92 (P20-P50) % -1., // 93 (P50-P51) % 1., // 94 (P26-P51) % -1.732050807568877, // 95 (P24-P51) % -1.732050807568877, // 96 (P51-P52) % 0., // 97 (P30-P52) % -1., // 98 (P28-P52) % -2., // 99 (P52-P53) % -1., // 100 (P34-P53) % 0., // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % -1.732050807568877, // 103 (P38-P54) % 1., // 104 (P36-P54) % -1., // 105 (P54-P55) % -2., // 106 (P42-P55) % 1.732050807568877, // 107 (P40-P55) % 1.732050807568877, // 108 (P46-P56) % -1., // 109 (P4-P56) % 1.732050807568877, // 110 (P56-P57) % 1., // 111 (P5-P57) % 1., // 112 (P57-P58) % -1., // 113 (P5-P58) % 0., // 114 (P45-P58) % 0., // 115 (P57-P59) % -1., // 116 (P58-P59) % -1.732050807568877, // 117 (P59-P60) % 2., // 118 (P44-P60) % 0., // 119 (P55-P60) % 1., // 120 (P56-P60) % ], % ]; %Beweglichkeiten=[ % [ // 0 % -0.5773502691896255, // 1 % -1., // 2 % -0.5773502691896255, // 3 % 0.3333333333333333, // 4 % -1.732050807568877, // 5 % -0.3333333333333333, // 6 % -1.732050807568877, // 7 % 1., // 8 % -0.5773502691896255, // 9 % 1.666666666666667, // 10 % 0.5773502691896255, // 11 % -1., // 12 % 0., // 13 % 0., // 14 % 1.154700538379251, // 15 % 0., // 16 % 0.5773502691896255, // 17 % 1., // 18 % -0.5773502691896255, // 19 % 1.666666666666667, // 20 % -0.5773502691896255, // 21 % 0.3333333333333333, // 22 % -1.732050807568877, // 23 % 1., // 24 % -1.732050807568877, // 25 % -0.3333333333333333, // 26 % -1.154700538379251, // 27 % -1.333333333333333, // 28 % -0.5773502691896255, // 29 % -0.3333333333333333, // 30 % 0., // 31 % -1.333333333333333, // 32 % 0.5773502691896255, // 33 % -0.3333333333333333, // 34 % 0.5773502691896255, // 35 % 1., // 36 % -0.5773502691896255, // 37 % 0.3333333333333333, // 38 % -0.5773502691896255, // 39 % 1.666666666666667, // 40 % -1.732050807568877, // 41 % 1., // 42 % -2.309401076758502, // 43 % 0., // 44 % -1.154700538379251, // 45 % 0., // 46 % -1.732050807568877, // 47 % -1., // 48 % -0.5773502691896255, // 49 % -1., // 50 % 0.5773502691896255, // 51 % -0.3333333333333333, // 52 % -0.5773502691896255, // 53 % 0.3333333333333333, // 54 % 0.5773502691896255, // 55 % 1., // 56 % -0.5773502691896255, // 57 % 1.666666666666667, // 58 % -1.732050807568877, // 59 % 1.666666666666667, // 60 % -1.154700538379251, // 61 % 0.6666666666666666, // 62 % -2.309401076758502, // 63 % 0.6666666666666666, // 64 % -1.732050807568877, // 65 % -0.3333333333333333, // 66 % -0.5773502691896255, // 67 % -1., // 68 % -0.5773502691896255, // 69 % 0.3333333333333333, // 70 % 0.5773502691896255, // 71 % -0.3333333333333333, // 72 % 0.5773502691896255, // 73 % 1., // 74 % 0., // 75 % 2., // 76 % -0.5773502691896255, // 77 % 1., // 78 % -1.154700538379251, // 79 % 2., // 80 % -1.732050807568877, // 81 % 1., // 82 % -1.732050807568877, // 83 % -0.3333333333333333, // 84 % -0.5773502691896255, // 85 % 0.3333333333333333, // 86 % -0.5773502691896255, // 87 % -1., // 88 % 0.5773502691896255, // 89 % -0.3333333333333333, // 90 % -0.5773502691896255, // 91 % -0.3333333333333333, // 92 % 0., // 93 % 0.6666666666666666, // 94 % -1.154700538379251, // 95 % 0., // 96 % 0., // 97 % 0., // 98 % -1.154700538379251, // 99 % 0.6666666666666666, // 100 % -0.5773502691896255, // 101 % -0.3333333333333333, // 102 % -0.5773502691896255, // 103 % 1., // 104 % -1.154700538379251, // 105 % 0., // 106 % 0., // 107 % 0.6666666666666666, // 108 % -1.154700538379251, // 109 % 0.6666666666666666, // 110 % -0.5773502691896255, // 111 % 1., // 112 % 0.5773502691896255, // 113 % 1.666666666666667, // 114 % 0., // 115 % 0.6666666666666666, // 116 % 1.154700538379251, // 117 % 0.6666666666666666, // 118 % 0., // 119 % 0., // 120 % ], % [ // 1 % 1., // 1 % -1.732050807568877, // 2 % 1., // 3 % -0.5773502691896255, // 4 % 0., // 5 % -1.154700538379251, // 6 % 0., // 7 % 0., // 8 % 1., // 9 % 0.5773502691896255, // 10 % 1., // 11 % -1.732050807568877, // 12 % 1., // 13 % -1.732050807568877, // 14 % 1., // 15 % -1.732050807568877, // 16 % 1., // 17 % -1.732050807568877, // 18 % 0., // 19 % -1.154700538379251, // 20 % 0., // 21 % -2.309401076758502, // 22 % -1., // 23 % -1.732050807568877, // 24 % -1., // 25 % -2.886751345948127, // 26 % -1., // 27 % -2.886751345948127, // 28 % -1., // 29 % -2.886751345948127, // 30 % -1., // 31 % -2.886751345948127, // 32 % -1., // 33 % -2.886751345948127, // 34 % -1., // 35 % -1.732050807568877, // 36 % -2., // 37 % -2.309401076758502, // 38 % -2., // 39 % -1.154700538379251, // 40 % -3., // 41 % -1.732050807568877, // 42 % -3., // 43 % -1.732050807568877, // 44 % -3., // 45 % -1.732050807568877, // 46 % -3., // 47 % -1.732050807568877, // 48 % -3., // 49 % -1.732050807568877, // 50 % -2., // 51 % -1.154700538379251, // 52 % -3., // 53 % -0.5773502691896255, // 54 % -2., // 55 % 0., // 56 % -3., // 57 % 0.5773502691896255, // 58 % -3., // 59 % 0.5773502691896255, // 60 % -3., // 61 % 0.5773502691896255, // 62 % -3., // 63 % 0.5773502691896255, // 64 % -3., // 65 % 0.5773502691896255, // 66 % -2., // 67 % 0., // 68 % -2., // 69 % 1.154700538379251, // 70 % -1., // 71 % 0.5773502691896255, // 72 % -1., // 73 % 1.732050807568877, // 74 % -1., // 75 % 1.732050807568877, // 76 % -1., // 77 % 1.732050807568877, // 78 % -1., // 79 % 1.732050807568877, // 80 % -1., // 81 % 1.732050807568877, // 82 % -1., // 83 % 0.5773502691896255, // 84 % 0., // 85 % 1.154700538379251, // 86 % 0., // 87 % 0., // 88 % 1., // 89 % 0.5773502691896255, // 90 % 0., // 91 % -1.154700538379251, // 92 % 0., // 93 % -1.154700538379251, // 94 % -1., // 95 % -1.732050807568877, // 96 % -1., // 97 % -1.732050807568877, // 98 % -2., // 99 % -1.154700538379251, // 100 % -2., // 101 % -1.154700538379251, // 102 % -2., // 103 % 0., // 104 % -2., // 105 % 0., // 106 % -1., // 107 % 0.5773502691896255, // 108 % -1., // 109 % 0.5773502691896255, // 110 % 0., // 111 % 0., // 112 % 1., // 113 % 0.5773502691896255, // 114 % 1., // 115 % 0.5773502691896255, // 116 % 1., // 117 % 0.5773502691896255, // 118 % 0., // 119 % 0., // 120 % ], % [ // 2 % 0., // 1 % 1.732050807568877, // 2 % 0., // 3 % 0.5773502691896255, // 4 % 1., // 5 % 1.154700538379251, // 6 % 1., // 7 % 0., // 8 % 0., // 9 % -0.5773502691896255, // 10 % 0., // 11 % 1.732050807568877, // 12 % 0., // 13 % 1.732050807568877, // 14 % 0., // 15 % 1.732050807568877, // 16 % 0., // 17 % 1.732050807568877, // 18 % 1., // 19 % 1.154700538379251, // 20 % 1., // 21 % 2.309401076758502, // 22 % 2., // 23 % 1.732050807568877, // 24 % 2., // 25 % 2.886751345948127, // 26 % 2., // 27 % 2.886751345948127, // 28 % 2., // 29 % 2.886751345948127, // 30 % 2., // 31 % 2.886751345948127, // 32 % 2., // 33 % 2.886751345948127, // 34 % 2., // 35 % 1.732050807568877, // 36 % 3., // 37 % 2.309401076758502, // 38 % 3., // 39 % 1.154700538379251, // 40 % 4., // 41 % 1.732050807568877, // 42 % 4., // 43 % 1.732050807568877, // 44 % 4., // 45 % 1.732050807568877, // 46 % 4., // 47 % 1.732050807568877, // 48 % 4., // 49 % 1.732050807568877, // 50 % 3., // 51 % 1.154700538379251, // 52 % 4., // 53 % 0.5773502691896255, // 54 % 3., // 55 % 0., // 56 % 4., // 57 % -0.5773502691896255, // 58 % 4., // 59 % -0.5773502691896255, // 60 % 4., // 61 % -0.5773502691896255, // 62 % 4., // 63 % -0.5773502691896255, // 64 % 4., // 65 % -0.5773502691896255, // 66 % 3., // 67 % 0., // 68 % 3., // 69 % -1.154700538379251, // 70 % 2., // 71 % -0.5773502691896255, // 72 % 2., // 73 % -1.732050807568877, // 74 % 2., // 75 % -1.732050807568877, // 76 % 2., // 77 % -1.732050807568877, // 78 % 2., // 79 % -1.732050807568877, // 80 % 2., // 81 % -1.732050807568877, // 82 % 2., // 83 % -0.5773502691896255, // 84 % 1., // 85 % -1.154700538379251, // 86 % 1., // 87 % 0., // 88 % 0., // 89 % -0.5773502691896255, // 90 % 1., // 91 % 1.154700538379251, // 92 % 1., // 93 % 1.154700538379251, // 94 % 2., // 95 % 1.732050807568877, // 96 % 2., // 97 % 1.732050807568877, // 98 % 3., // 99 % 1.154700538379251, // 100 % 3., // 101 % 1.154700538379251, // 102 % 3., // 103 % 0., // 104 % 3., // 105 % 0., // 106 % 2., // 107 % -0.5773502691896255, // 108 % 2., // 109 % -0.5773502691896255, // 110 % 1., // 111 % 0., // 112 % 0., // 113 % -0.5773502691896255, // 114 % 0., // 115 % -0.5773502691896255, // 116 % 0., // 117 % -0.5773502691896255, // 118 % 1., // 119 % 0., // 120 % ], % [ // 3 % 0.5773502691896255, // 1 % 2., // 2 % 0.5773502691896255, // 3 % 0.6666666666666666, // 4 % 1.732050807568877, // 5 % 1.333333333333333, // 6 % 1.732050807568877, // 7 % 0., // 8 % 0.5773502691896255, // 9 % -0.6666666666666666, // 10 % -0.5773502691896255, // 11 % 2., // 12 % 0., // 13 % 1., // 14 % -1.154700538379251, // 15 % 1., // 16 % -0.5773502691896255, // 17 % 0., // 18 % 0.5773502691896255, // 19 % -0.6666666666666666, // 20 % 0.5773502691896255, // 21 % 0.6666666666666666, // 22 % 1.732050807568877, // 23 % 0., // 24 % 1.732050807568877, // 25 % 1.333333333333333, // 26 % 1.154700538379251, // 27 % 2.333333333333333, // 28 % 0.5773502691896255, // 29 % 1.333333333333333, // 30 % 0., // 31 % 2.333333333333333, // 32 % -0.5773502691896255, // 33 % 1.333333333333333, // 34 % -0.5773502691896255, // 35 % 0., // 36 % 0.5773502691896255, // 37 % 0.6666666666666666, // 38 % 0.5773502691896255, // 39 % -0.6666666666666666, // 40 % 1.732050807568877, // 41 % 0., // 42 % 2.309401076758502, // 43 % 1., // 44 % 1.154700538379251, // 45 % 1., // 46 % 1.732050807568877, // 47 % 2., // 48 % 0.5773502691896255, // 49 % 2., // 50 % -0.5773502691896255, // 51 % 1.333333333333333, // 52 % 0.5773502691896255, // 53 % 0.6666666666666666, // 54 % -0.5773502691896255, // 55 % 0., // 56 % 0.5773502691896255, // 57 % -0.6666666666666666, // 58 % 1.732050807568877, // 59 % -0.6666666666666666, // 60 % 1.154700538379251, // 61 % 0.3333333333333333, // 62 % 2.309401076758502, // 63 % 0.3333333333333333, // 64 % 1.732050807568877, // 65 % 1.333333333333333, // 66 % 0.5773502691896255, // 67 % 2., // 68 % 0.5773502691896255, // 69 % 0.6666666666666666, // 70 % -0.5773502691896255, // 71 % 1.333333333333333, // 72 % -0.5773502691896255, // 73 % 0., // 74 % 0., // 75 % -1., // 76 % 0.5773502691896255, // 77 % 0., // 78 % 1.154700538379251, // 79 % -1., // 80 % 1.732050807568877, // 81 % 0., // 82 % 1.732050807568877, // 83 % 1.333333333333333, // 84 % 0.5773502691896255, // 85 % 0.6666666666666666, // 86 % 0.5773502691896255, // 87 % 2., // 88 % -0.5773502691896255, // 89 % 1.333333333333333, // 90 % 0.5773502691896255, // 91 % 1.333333333333333, // 92 % 0., // 93 % 0.3333333333333333, // 94 % 1.154700538379251, // 95 % 1., // 96 % 0., // 97 % 1., // 98 % 1.154700538379251, // 99 % 0.3333333333333333, // 100 % 0.5773502691896255, // 101 % 1.333333333333333, // 102 % 0.5773502691896255, // 103 % 0., // 104 % 1.154700538379251, // 105 % 1., // 106 % 0., // 107 % 0.3333333333333333, // 108 % 1.154700538379251, // 109 % 0.3333333333333333, // 110 % 0.5773502691896255, // 111 % 0., // 112 % -0.5773502691896255, // 113 % -0.6666666666666666, // 114 % 0., // 115 % 0.3333333333333333, // 116 % -1.154700538379251, // 117 % 0.3333333333333333, // 118 % 0., // 119 % 1., // 120 % ], % ]; %Vergleichsrichtung=[[1,0,0],[2,1,0]]; %Nenner=2; %DD=[ % [112,114], % [115,115], % [119,119], % [120,120], % ]; % %Beweglichkeitsgrad=1; %Einsetzkantenzahl=4; %Maxi=110; Maxj=49; MaxInvAij=42.78460969082653; //=Kante [ 56, 57 ] %gerechnet_mit_Button="acos(1/4)"; % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/6.60, 29/4.73/7.46, 30/4.73/6.46, 31/5.60/6.96, 32/5.60/5.96, 33/6.46/6.46, 34/5.96/5.60, 35/6.96/5.60, 36/6.46/4.73, 37/7.46/4.73, 38/6.60/4.23, 39/7.46/3.73, 40/6.60/3.23, 41/7.46/2.73, 42/6.46/2.73, 43/6.96/1.87, 44/5.96/1.87, 45/6.46/1.00, 46/3.23/1.87, 47/2.37/2.37, 48/1.87/3.23, 49/1.87/4.23, 50/2.37/5.10, 51/3.23/5.60, 52/4.23/5.60, 53/5.10/5.10, 54/5.60/4.23, 55/5.60/3.23, 56/4.23/1.87, 57/4.73/1.00, 58/5.60/0.50, 59/5.60/1.50, 60/5.10/2.37} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-2) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-2); \draw[line width=2,blue!50] (p-4) -- (p-3); \draw[line width=2,blue!50] (p-4) -- (p-2); \draw[line width=2,blue!50] (p-5) -- (p-4); \draw[line width=2,blue!50] (p-5) -- (p-2); \draw[line width=2,blue!50] (p-6) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-6); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-8); \draw[line width=2,blue!50] (p-11) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-12) -- (p-11); \draw[line width=2,blue!50] (p-12) -- (p-10); \draw[line width=2,blue!50] (p-13) -- (p-11); \draw[line width=2,blue!50] (p-13) -- (p-12); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-14); \draw[line width=2,blue!50] (p-16) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-18) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-19); \draw[line width=2,blue!50] (p-20) -- (p-18); \draw[line width=2,blue!50] (p-21) -- (p-19); \draw[line width=2,blue!50] (p-21) -- (p-20); \draw[line width=2,blue!50] (p-23) -- (p-21); \draw[line width=2,blue!50] (p-25) -- (p-23); \draw[line width=2,blue!50] (p-26) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-26); \draw[line width=2,blue!50] (p-28) -- (p-27); \draw[line width=2,blue!50] (p-28) -- (p-26); \draw[line width=2,blue!50] (p-29) -- (p-27); \draw[line width=2,blue!50] (p-29) -- (p-28); \draw[line width=2,blue!50] (p-30) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-30); \draw[line width=2,blue!50] (p-32) -- (p-31); \draw[line width=2,blue!50] (p-33) -- (p-31); \draw[line width=2,blue!50] (p-33) -- (p-32); \draw[line width=2,blue!50] (p-34) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-34); \draw[line width=2,blue!50] (p-36) -- (p-35); \draw[line width=2,blue!50] (p-36) -- (p-34); \draw[line width=2,blue!50] (p-37) -- (p-35); \draw[line width=2,blue!50] (p-38) -- (p-37); \draw[line width=2,blue!50] (p-39) -- (p-37); \draw[line width=2,blue!50] (p-39) -- (p-38); \draw[line width=2,blue!50] (p-40) -- (p-39); \draw[line width=2,blue!50] (p-41) -- (p-39); \draw[line width=2,blue!50] (p-41) -- (p-40); \draw[line width=2,blue!50] (p-42) -- (p-41); \draw[line width=2,blue!50] (p-43) -- (p-41); \draw[line width=2,blue!50] (p-43) -- (p-42); \draw[line width=2,blue!50] (p-44) -- (p-43); \draw[line width=2,blue!50] (p-44) -- (p-42); \draw[line width=2,blue!50] (p-45) -- (p-43); \draw[line width=2,blue!50] (p-45) -- (p-44); \draw[line width=2,blue!50] (p-46) -- (p-6); \draw[line width=2,blue!50] (p-46) -- (p-3); \draw[line width=2,blue!50] (p-46) -- (p-47); \draw[line width=2,blue!50] (p-47) -- (p-10); \draw[line width=2,blue!50] (p-47) -- (p-8); \draw[line width=2,blue!50] (p-47) -- (p-48); \draw[line width=2,blue!50] (p-48) -- (p-14); \draw[line width=2,blue!50] (p-48) -- (p-12); \draw[line width=2,blue!50] (p-48) -- (p-49); \draw[line width=2,blue!50] (p-49) -- (p-16); \draw[line width=2,blue!50] (p-49) -- (p-50); \draw[line width=2,blue!50] (p-50) -- (p-20); \draw[line width=2,blue!50] (p-50) -- (p-51); \draw[line width=2,blue!50] (p-51) -- (p-26); \draw[line width=2,blue!50] (p-51) -- (p-52); \draw[line width=2,blue!50] (p-52) -- (p-30); \draw[line width=2,blue!50] (p-52) -- (p-53); \draw[line width=2,blue!50] (p-53) -- (p-34); \draw[line width=2,blue!50] (p-53) -- (p-32); \draw[line width=2,blue!50] (p-53) -- (p-54); \draw[line width=2,blue!50] (p-54) -- (p-38); \draw[line width=2,blue!50] (p-54) -- (p-36); \draw[line width=2,blue!50] (p-54) -- (p-55); \draw[line width=2,blue!50] (p-55) -- (p-42); \draw[line width=2,blue!50] (p-55) -- (p-40); \draw[line width=2,blue!50] (p-58) -- (p-5); \draw[line width=2,blue!50] (p-58) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 2 (orange): $ %Eingabe war: % %Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2); N(46,6,3); N(47,10,8); N(48,14,12); N(49,18,16); N(50,22,20); N(51,26,24); N(52,30,28); N(53,34,32); N(54,38,36); N(55,42,40); N(56,46,4); N(57,56,5); L(58,57,5); L(59,57,58); N(60,44,55); A(58,45,Bew(5)); A(45,59,Bew(6)); A(59,60,Bew(6)); A(46,47,Bew(6)); A(47,48,Bew(6)); A(48,49,Bew(6)); A(49,50,Bew(6)); A(50,51,Bew(6)); A(51,52,Bew(6)); A(52,53,Bew(6)); A(53,54,Bew(6)); A(54,55,Bew(6)); A(60,56,Bew(6)); W(); % % % % % %Belastungsarray=[ % [ // 0 % 1.732050807568877, // 1 (P1-P2) % -1.732050807568877, // 2 (P1-P3) % -0.5773502691896255, // 3 (P2-P3) % -0.5773502691896255, // 4 (P3-P4) % 0.5773502691896255, // 5 (P2-P4) % -0.5773502691896255, // 6 (P4-P5) % 1.154700538379251, // 7 (P2-P5) % 1., // 8 (P1-P6) % 1., // 9 (P1-P7) % 1., // 10 (P6-P7) % -1., // 11 (P7-P8) % 0., // 12 (P6-P8) % 2., // 13 (P7-P9) % -1., // 14 (P8-P9) % 0., // 15 (P9-P10) % 1.732050807568877, // 16 (P9-P11) % 1.154700538379251, // 17 (P10-P11) % -1.154700538379251, // 18 (P11-P12) % -0.5773502691896255, // 19 (P10-P12) % 2.886751345948127, // 20 (P11-P13) % -2.309401076758502, // 21 (P12-P13) % 1., // 22 (P13-P14) % 2., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 0., // 26 (P14-P16) % 3., // 27 (P15-P17) % -1., // 28 (P16-P17) % -0.5773502691896255, // 29 (P17-P18) % 2.886751345948127, // 30 (P17-P19) % 0.5773502691896255, // 31 (P18-P19) % -0.5773502691896255, // 32 (P19-P20) % -0.5773502691896255, // 33 (P18-P20) % 3.464101615137753, // 34 (P19-P21) % -1.732050807568877, // 35 (P20-P21) % 0., // 36 (P21-P22) % 3., // 37 (P21-P23) % 0., // 38 (P22-P23) % 0., // 39 (P23-P24) % 0., // 40 (P22-P24) % 3., // 41 (P23-P25) % 0., // 42 (P24-P25) % -1.732050807568877, // 43 (P25-P26) % 3.464101615137753, // 44 (P25-P27) % -0.5773502691896255, // 45 (P26-P27) % 0.5773502691896255, // 46 (P27-P28) % -0.5773502691896255, // 47 (P26-P28) % 2.886751345948127, // 48 (P27-P29) % -0.5773502691896255, // 49 (P28-P29) % -1., // 50 (P29-P30) % 3., // 51 (P29-P31) % -1., // 52 (P30-P31) % 1., // 53 (P31-P32) % 0., // 54 (P30-P32) % 2., // 55 (P31-P33) % 1., // 56 (P32-P33) % -2.309401076758502, // 57 (P33-P34) % 2.886751345948127, // 58 (P33-P35) % -1.154700538379251, // 59 (P34-P35) % 1.154700538379251, // 60 (P35-P36) % -0.5773502691896255, // 61 (P34-P36) % 1.732050807568877, // 62 (P35-P37) % 0., // 63 (P36-P37) % -1., // 64 (P37-P38) % 2., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 0., // 68 (P38-P40) % 1., // 69 (P39-P41) % 1., // 70 (P40-P41) % -1.732050807568877, // 71 (P41-P42) % 1.732050807568877, // 72 (P41-P43) % -0.5773502691896255, // 73 (P42-P43) % 0.5773502691896255, // 74 (P43-P44) % -0.5773502691896255, // 75 (P42-P44) % 1.154700538379251, // 76 (P43-P45) % -0.5773502691896255, // 77 (P44-P45) % 0., // 78 (P45-P59) % 1.732050807568877, // 79 (P6-P46) % -2., // 80 (P3-P46) % -1., // 81 (P46-P47) % 1., // 82 (P10-P47) % -1.732050807568877, // 83 (P8-P47) % -1.732050807568877, // 84 (P47-P48) % 1.732050807568877, // 85 (P14-P48) % -3., // 86 (P12-P48) % -3., // 87 (P48-P49) % 0., // 88 (P18-P49) % -1.732050807568877, // 89 (P16-P49) % -3.464101615137753, // 90 (P49-P50) % 0., // 91 (P22-P50) % -2., // 92 (P20-P50) % -4., // 93 (P50-P51) % -2., // 94 (P26-P51) % 0., // 95 (P24-P51) % -3.464101615137753, // 96 (P51-P52) % -1.732050807568877, // 97 (P30-P52) % 0., // 98 (P28-P52) % -3., // 99 (P52-P53) % -3., // 100 (P34-P53) % 1.732050807568877, // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % -1.732050807568877, // 103 (P38-P54) % 1., // 104 (P36-P54) % -1., // 105 (P54-P55) % -2., // 106 (P42-P55) % 1.732050807568877, // 107 (P40-P55) % 0., // 108 (P46-P56) % 0., // 109 (P4-P56) % 0., // 110 (P56-P57) % 0., // 111 (P5-P57) % 0., // 112 (P57-P58) % 1., // 113 (P5-P58) % 1., // 114 (P45-P58) % 0., // 115 (P57-P59) % 0., // 116 (P58-P59) % 0., // 117 (P59-P60) % 0., // 118 (P44-P60) % 0., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 1 % 0., // 1 (P1-P2) % -1.732050807568877, // 2 (P1-P3) % 0.5773502691896255, // 3 (P2-P3) % -1.154700538379251, // 4 (P3-P4) % -0.5773502691896255, // 5 (P2-P4) % -2.886751345948127, // 6 (P4-P5) % 0.5773502691896255, // 7 (P2-P5) % 2., // 8 (P1-P6) % -1., // 9 (P1-P7) % 0., // 10 (P6-P7) % 0., // 11 (P7-P8) % 1., // 12 (P6-P8) % -1., // 13 (P7-P9) % 2., // 14 (P8-P9) % -1.732050807568877, // 15 (P9-P10) % 0., // 16 (P9-P11) % 0.5773502691896255, // 17 (P10-P11) % -0.5773502691896255, // 18 (P11-P12) % -1.154700538379251, // 19 (P10-P12) % 0.5773502691896255, // 20 (P11-P13) % -2.886751345948127, // 21 (P12-P13) % 3., // 22 (P13-P14) % -1., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 1., // 26 (P14-P16) % 0., // 27 (P15-P17) % 1., // 28 (P16-P17) % -1.154700538379251, // 29 (P17-P18) % 0.5773502691896255, // 30 (P17-P19) % 1.154700538379251, // 31 (P18-P19) % -1.154700538379251, // 32 (P19-P20) % -1.154700538379251, // 33 (P18-P20) % 1.732050807568877, // 34 (P19-P21) % -3.464101615137753, // 35 (P20-P21) % 3., // 36 (P21-P22) % 0., // 37 (P21-P23) % 1., // 38 (P22-P23) % -1., // 39 (P23-P24) % 1., // 40 (P22-P24) % 1., // 41 (P23-P25) % 1., // 42 (P24-P25) % -1.732050807568877, // 43 (P25-P26) % 1.732050807568877, // 44 (P25-P27) % 0.5773502691896255, // 45 (P26-P27) % -0.5773502691896255, // 46 (P27-P28) % -1.154700538379251, // 47 (P26-P28) % 2.309401076758502, // 48 (P27-P29) % -2.886751345948127, // 49 (P28-P29) % 2., // 50 (P29-P30) % 1., // 51 (P29-P31) % 0., // 52 (P30-P31) % 0., // 53 (P31-P32) % 1., // 54 (P30-P32) % 1., // 55 (P31-P33) % 2., // 56 (P32-P33) % -2.886751345948127, // 57 (P33-P34) % 2.309401076758502, // 58 (P33-P35) % -0.5773502691896255, // 59 (P34-P35) % 0.5773502691896255, // 60 (P35-P36) % -1.154700538379251, // 61 (P34-P36) % 1.732050807568877, // 62 (P35-P37) % -1.732050807568877, // 63 (P36-P37) % 1., // 64 (P37-P38) % 1., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 1., // 68 (P38-P40) % 0., // 69 (P39-P41) % 3., // 70 (P40-P41) % -3.464101615137753, // 71 (P41-P42) % 1.732050807568877, // 72 (P41-P43) % -1.154700538379251, // 73 (P42-P43) % 1.154700538379251, // 74 (P43-P44) % -1.154700538379251, // 75 (P42-P44) % 0.5773502691896255, // 76 (P43-P45) % -1.154700538379251, // 77 (P44-P45) % 1., // 78 (P45-P59) % 1.732050807568877, // 79 (P6-P46) % -1., // 80 (P3-P46) % 1., // 81 (P46-P47) % -1., // 82 (P10-P47) % 1.732050807568877, // 83 (P8-P47) % 1.732050807568877, // 84 (P47-P48) % 3.464101615137753, // 85 (P14-P48) % -3., // 86 (P12-P48) % 0., // 87 (P48-P49) % 0., // 88 (P18-P49) % 0., // 89 (P16-P49) % 0., // 90 (P49-P50) % 3.464101615137753, // 91 (P22-P50) % -4., // 92 (P20-P50) % -2., // 93 (P50-P51) % -1., // 94 (P26-P51) % 0., // 95 (P24-P51) % -1.732050807568877, // 96 (P51-P52) % 1.732050807568877, // 97 (P30-P52) % -3., // 98 (P28-P52) % -3., // 99 (P52-P53) % -3., // 100 (P34-P53) % 1.732050807568877, // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % 0., // 103 (P38-P54) % -1., // 104 (P36-P54) % -2., // 105 (P54-P55) % -4., // 106 (P42-P55) % 3.464101615137753, // 107 (P40-P55) % 1.732050807568877, // 108 (P46-P56) % -3., // 109 (P4-P56) % 3.464101615137753, // 110 (P56-P57) % 3., // 111 (P5-P57) % 1., // 112 (P57-P58) % -1., // 113 (P5-P58) % 0., // 114 (P45-P58) % 1., // 115 (P57-P59) % -1., // 116 (P58-P59) % 0., // 117 (P59-P60) % 0., // 118 (P44-P60) % 0., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 2 % 2., // 1 (P1-P2) % -2., // 2 (P1-P3) % -1.333333333333333, // 3 (P2-P3) % -0.3333333333333333, // 4 (P3-P4) % 1.333333333333333, // 5 (P2-P4) % 0.6666666666666666, // 6 (P4-P5) % 0.6666666666666666, // 7 (P2-P5) % 1.154700538379251, // 8 (P1-P6) % 1.154700538379251, // 9 (P1-P7) % 1.154700538379251, // 10 (P6-P7) % -1.154700538379251, // 11 (P7-P8) % 0., // 12 (P6-P8) % 2.309401076758502, // 13 (P7-P9) % -1.154700538379251, // 14 (P8-P9) % 0., // 15 (P9-P10) % 2., // 16 (P9-P11) % 0.6666666666666666, // 17 (P10-P11) % -0.6666666666666666, // 18 (P11-P12) % -0.3333333333333333, // 19 (P10-P12) % 2.666666666666667, // 20 (P11-P13) % -1.333333333333333, // 21 (P12-P13) % 0., // 22 (P13-P14) % 2.309401076758502, // 23 (P13-P15) % 0., // 24 (P14-P15) % 0., // 25 (P15-P16) % 0., // 26 (P14-P16) % 2.309401076758502, // 27 (P15-P17) % 0., // 28 (P16-P17) % -1.333333333333333, // 29 (P17-P18) % 2.666666666666667, // 30 (P17-P19) % -0.6666666666666666, // 31 (P18-P19) % 0.6666666666666666, // 32 (P19-P20) % -0.3333333333333333, // 33 (P18-P20) % 2., // 34 (P19-P21) % 0., // 35 (P20-P21) % -1.154700538379251, // 36 (P21-P22) % 2.309401076758502, // 37 (P21-P23) % -1.154700538379251, // 38 (P22-P23) % 1.154700538379251, // 39 (P23-P24) % 0., // 40 (P22-P24) % 1.154700538379251, // 41 (P23-P25) % 1.154700538379251, // 42 (P24-P25) % -2., // 43 (P25-P26) % 2., // 44 (P25-P27) % -1.333333333333333, // 45 (P26-P27) % 1.333333333333333, // 46 (P27-P28) % -0.3333333333333333, // 47 (P26-P28) % 0.6666666666666666, // 48 (P27-P29) % 0.6666666666666666, // 49 (P28-P29) % -1.154700538379251, // 50 (P29-P30) % 1.154700538379251, // 51 (P29-P31) % -1.154700538379251, // 52 (P30-P31) % 1.154700538379251, // 53 (P31-P32) % 0., // 54 (P30-P32) % 0., // 55 (P31-P33) % 1.154700538379251, // 56 (P32-P33) % -1.333333333333333, // 57 (P33-P34) % 0.6666666666666666, // 58 (P33-P35) % -0.6666666666666666, // 59 (P34-P35) % 0.6666666666666666, // 60 (P35-P36) % -0.3333333333333333, // 61 (P34-P36) % 0., // 62 (P35-P37) % 0., // 63 (P36-P37) % 0., // 64 (P37-P38) % 0., // 65 (P37-P39) % 0., // 66 (P38-P39) % 0., // 67 (P39-P40) % 0., // 68 (P38-P40) % 0., // 69 (P39-P41) % 0., // 70 (P40-P41) % 0., // 71 (P41-P42) % 0., // 72 (P41-P43) % 0.6666666666666666, // 73 (P42-P43) % -0.6666666666666666, // 74 (P43-P44) % -0.3333333333333333, // 75 (P42-P44) % 0.6666666666666666, // 76 (P43-P45) % -1.333333333333333, // 77 (P44-P45) % 1.154700538379251, // 78 (P45-P59) % 2., // 79 (P6-P46) % -2.886751345948127, // 80 (P3-P46) % -2.309401076758502, // 81 (P46-P47) % 0.5773502691896255, // 82 (P10-P47) % -2., // 83 (P8-P47) % -3., // 84 (P47-P48) % 0., // 85 (P14-P48) % -1.732050807568877, // 86 (P12-P48) % -3.464101615137753, // 87 (P48-P49) % -1.732050807568877, // 88 (P18-P49) % 0., // 89 (P16-P49) % -3., // 90 (P49-P50) % -2., // 91 (P22-P50) % 0.5773502691896255, // 92 (P20-P50) % -2.309401076758502, // 93 (P50-P51) % -2.886751345948127, // 94 (P26-P51) % 2., // 95 (P24-P51) % -1., // 96 (P51-P52) % -2., // 97 (P30-P52) % 1.732050807568877, // 98 (P28-P52) % 0., // 99 (P52-P53) % -1.732050807568877, // 100 (P34-P53) % 2., // 101 (P32-P53) % 1., // 102 (P53-P54) % 0., // 103 (P38-P54) % 0.5773502691896255, // 104 (P36-P54) % 1.154700538379251, // 105 (P54-P55) % 0.5773502691896255, // 106 (P42-P55) % 0., // 107 (P40-P55) % -1., // 108 (P46-P56) % 1.732050807568877, // 109 (P4-P56) % -2., // 110 (P56-P57) % -1.154700538379251, // 111 (P5-P57) % -1.154700538379251, // 112 (P57-P58) % 1.154700538379251, // 113 (P5-P58) % 0., // 114 (P45-P58) % 0., // 115 (P57-P59) % 1.154700538379251, // 116 (P58-P59) % 2., // 117 (P59-P60) % -1.732050807568877, // 118 (P44-P60) % 1., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 3 % -1.154700538379251, // 1 (P1-P2) % 0.5773502691896255, // 2 (P1-P3) % 0.5773502691896255, // 3 (P2-P3) % 0., // 4 (P3-P4) % -0.5773502691896255, // 5 (P2-P4) % -0.5773502691896255, // 6 (P4-P5) % -0.5773502691896255, // 7 (P2-P5) % 0., // 8 (P1-P6) % -1., // 9 (P1-P7) % 0., // 10 (P6-P7) % 0., // 11 (P7-P8) % 0., // 12 (P6-P8) % -1., // 13 (P7-P9) % 0., // 14 (P8-P9) % 0.5773502691896255, // 15 (P9-P10) % -1.154700538379251, // 16 (P9-P11) % 0.5773502691896255, // 17 (P10-P11) % -0.5773502691896255, // 18 (P11-P12) % 0., // 19 (P10-P12) % -0.5773502691896255, // 20 (P11-P13) % -0.5773502691896255, // 21 (P12-P13) % 1., // 22 (P13-P14) % -1., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 0., // 26 (P14-P16) % 0., // 27 (P15-P17) % -1., // 28 (P16-P17) % 1.154700538379251, // 29 (P17-P18) % -0.5773502691896255, // 30 (P17-P19) % 1.154700538379251, // 31 (P18-P19) % -1.154700538379251, // 32 (P19-P20) % 0., // 33 (P18-P20) % 0.5773502691896255, // 34 (P19-P21) % -1.154700538379251, // 35 (P20-P21) % 1., // 36 (P21-P22) % 0., // 37 (P21-P23) % 1., // 38 (P22-P23) % -1., // 39 (P23-P24) % 0., // 40 (P22-P24) % 1., // 41 (P23-P25) % -1., // 42 (P24-P25) % 0.5773502691896255, // 43 (P25-P26) % 0.5773502691896255, // 44 (P25-P27) % 0.5773502691896255, // 45 (P26-P27) % -0.5773502691896255, // 46 (P27-P28) % 0., // 47 (P26-P28) % 1.154700538379251, // 48 (P27-P29) % -0.5773502691896255, // 49 (P28-P29) % 0., // 50 (P29-P30) % 1., // 51 (P29-P31) % 0., // 52 (P30-P31) % 0., // 53 (P31-P32) % 0., // 54 (P30-P32) % 1., // 55 (P31-P33) % 0., // 56 (P32-P33) % -0.5773502691896255, // 57 (P33-P34) % 1.154700538379251, // 58 (P33-P35) % -0.5773502691896255, // 59 (P34-P35) % 0.5773502691896255, // 60 (P35-P36) % 0., // 61 (P34-P36) % 0.5773502691896255, // 62 (P35-P37) % 0.5773502691896255, // 63 (P36-P37) % -1., // 64 (P37-P38) % 1., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 0., // 68 (P38-P40) % 0., // 69 (P39-P41) % 1., // 70 (P40-P41) % -1.154700538379251, // 71 (P41-P42) % 0.5773502691896255, // 72 (P41-P43) % -1.154700538379251, // 73 (P42-P43) % 1.154700538379251, // 74 (P43-P44) % 0., // 75 (P42-P44) % -0.5773502691896255, // 76 (P43-P45) % 1.154700538379251, // 77 (P44-P45) % -1., // 78 (P45-P59) % 0., // 79 (P6-P46) % 1., // 80 (P3-P46) % 2., // 81 (P46-P47) % 1., // 82 (P10-P47) % 0., // 83 (P8-P47) % 1.732050807568877, // 84 (P47-P48) % 1.732050807568877, // 85 (P14-P48) % -1., // 86 (P12-P48) % 1., // 87 (P48-P49) % 2., // 88 (P18-P49) % -1.732050807568877, // 89 (P16-P49) % 0., // 90 (P49-P50) % 1.732050807568877, // 91 (P22-P50) % -2., // 92 (P20-P50) % -1., // 93 (P50-P51) % 1., // 94 (P26-P51) % -1.732050807568877, // 95 (P24-P51) % -1.732050807568877, // 96 (P51-P52) % 0., // 97 (P30-P52) % -1., // 98 (P28-P52) % -2., // 99 (P52-P53) % -1., // 100 (P34-P53) % 0., // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % -1.732050807568877, // 103 (P38-P54) % 1., // 104 (P36-P54) % -1., // 105 (P54-P55) % -2., // 106 (P42-P55) % 1.732050807568877, // 107 (P40-P55) % 1.732050807568877, // 108 (P46-P56) % -1., // 109 (P4-P56) % 1.732050807568877, // 110 (P56-P57) % 1., // 111 (P5-P57) % 1., // 112 (P57-P58) % -1., // 113 (P5-P58) % 0., // 114 (P45-P58) % 0., // 115 (P57-P59) % -1., // 116 (P58-P59) % -1.732050807568877, // 117 (P59-P60) % 2., // 118 (P44-P60) % 0., // 119 (P55-P60) % 1., // 120 (P56-P60) % ], % ]; %Beweglichkeiten=[ % [ // 0 % -0.5773502691896255, // 1 % -1., // 2 % -0.5773502691896255, // 3 % 0.3333333333333333, // 4 % -1.732050807568877, // 5 % -0.3333333333333333, // 6 % -1.732050807568877, // 7 % 1., // 8 % -0.5773502691896255, // 9 % 1.666666666666667, // 10 % 0.5773502691896255, // 11 % -1., // 12 % 0., // 13 % 0., // 14 % 1.154700538379251, // 15 % 0., // 16 % 0.5773502691896255, // 17 % 1., // 18 % -0.5773502691896255, // 19 % 1.666666666666667, // 20 % -0.5773502691896255, // 21 % 0.3333333333333333, // 22 % -1.732050807568877, // 23 % 1., // 24 % -1.732050807568877, // 25 % -0.3333333333333333, // 26 % -1.154700538379251, // 27 % -1.333333333333333, // 28 % -0.5773502691896255, // 29 % -0.3333333333333333, // 30 % 0., // 31 % -1.333333333333333, // 32 % 0.5773502691896255, // 33 % -0.3333333333333333, // 34 % 0.5773502691896255, // 35 % 1., // 36 % -0.5773502691896255, // 37 % 0.3333333333333333, // 38 % -0.5773502691896255, // 39 % 1.666666666666667, // 40 % -1.732050807568877, // 41 % 1., // 42 % -2.309401076758502, // 43 % 0., // 44 % -1.154700538379251, // 45 % 0., // 46 % -1.732050807568877, // 47 % -1., // 48 % -0.5773502691896255, // 49 % -1., // 50 % 0.5773502691896255, // 51 % -0.3333333333333333, // 52 % -0.5773502691896255, // 53 % 0.3333333333333333, // 54 % 0.5773502691896255, // 55 % 1., // 56 % -0.5773502691896255, // 57 % 1.666666666666667, // 58 % -1.732050807568877, // 59 % 1.666666666666667, // 60 % -1.154700538379251, // 61 % 0.6666666666666666, // 62 % -2.309401076758502, // 63 % 0.6666666666666666, // 64 % -1.732050807568877, // 65 % -0.3333333333333333, // 66 % -0.5773502691896255, // 67 % -1., // 68 % -0.5773502691896255, // 69 % 0.3333333333333333, // 70 % 0.5773502691896255, // 71 % -0.3333333333333333, // 72 % 0.5773502691896255, // 73 % 1., // 74 % 0., // 75 % 2., // 76 % -0.5773502691896255, // 77 % 1., // 78 % -1.154700538379251, // 79 % 2., // 80 % -1.732050807568877, // 81 % 1., // 82 % -1.732050807568877, // 83 % -0.3333333333333333, // 84 % -0.5773502691896255, // 85 % 0.3333333333333333, // 86 % -0.5773502691896255, // 87 % -1., // 88 % 0.5773502691896255, // 89 % -0.3333333333333333, // 90 % -0.5773502691896255, // 91 % -0.3333333333333333, // 92 % 0., // 93 % 0.6666666666666666, // 94 % -1.154700538379251, // 95 % 0., // 96 % 0., // 97 % 0., // 98 % -1.154700538379251, // 99 % 0.6666666666666666, // 100 % -0.5773502691896255, // 101 % -0.3333333333333333, // 102 % -0.5773502691896255, // 103 % 1., // 104 % -1.154700538379251, // 105 % 0., // 106 % 0., // 107 % 0.6666666666666666, // 108 % -1.154700538379251, // 109 % 0.6666666666666666, // 110 % -0.5773502691896255, // 111 % 1., // 112 % 0.5773502691896255, // 113 % 1.666666666666667, // 114 % 0., // 115 % 0.6666666666666666, // 116 % 1.154700538379251, // 117 % 0.6666666666666666, // 118 % 0., // 119 % 0., // 120 % ], % [ // 1 % 1., // 1 % -1.732050807568877, // 2 % 1., // 3 % -0.5773502691896255, // 4 % 0., // 5 % -1.154700538379251, // 6 % 0., // 7 % 0., // 8 % 1., // 9 % 0.5773502691896255, // 10 % 1., // 11 % -1.732050807568877, // 12 % 1., // 13 % -1.732050807568877, // 14 % 1., // 15 % -1.732050807568877, // 16 % 1., // 17 % -1.732050807568877, // 18 % 0., // 19 % -1.154700538379251, // 20 % 0., // 21 % -2.309401076758502, // 22 % -1., // 23 % -1.732050807568877, // 24 % -1., // 25 % -2.886751345948127, // 26 % -1., // 27 % -2.886751345948127, // 28 % -1., // 29 % -2.886751345948127, // 30 % -1., // 31 % -2.886751345948127, // 32 % -1., // 33 % -2.886751345948127, // 34 % -1., // 35 % -1.732050807568877, // 36 % -2., // 37 % -2.309401076758502, // 38 % -2., // 39 % -1.154700538379251, // 40 % -3., // 41 % -1.732050807568877, // 42 % -3., // 43 % -1.732050807568877, // 44 % -3., // 45 % -1.732050807568877, // 46 % -3., // 47 % -1.732050807568877, // 48 % -3., // 49 % -1.732050807568877, // 50 % -2., // 51 % -1.154700538379251, // 52 % -3., // 53 % -0.5773502691896255, // 54 % -2., // 55 % 0., // 56 % -3., // 57 % 0.5773502691896255, // 58 % -3., // 59 % 0.5773502691896255, // 60 % -3., // 61 % 0.5773502691896255, // 62 % -3., // 63 % 0.5773502691896255, // 64 % -3., // 65 % 0.5773502691896255, // 66 % -2., // 67 % 0., // 68 % -2., // 69 % 1.154700538379251, // 70 % -1., // 71 % 0.5773502691896255, // 72 % -1., // 73 % 1.732050807568877, // 74 % -1., // 75 % 1.732050807568877, // 76 % -1., // 77 % 1.732050807568877, // 78 % -1., // 79 % 1.732050807568877, // 80 % -1., // 81 % 1.732050807568877, // 82 % -1., // 83 % 0.5773502691896255, // 84 % 0., // 85 % 1.154700538379251, // 86 % 0., // 87 % 0., // 88 % 1., // 89 % 0.5773502691896255, // 90 % 0., // 91 % -1.154700538379251, // 92 % 0., // 93 % -1.154700538379251, // 94 % -1., // 95 % -1.732050807568877, // 96 % -1., // 97 % -1.732050807568877, // 98 % -2., // 99 % -1.154700538379251, // 100 % -2., // 101 % -1.154700538379251, // 102 % -2., // 103 % 0., // 104 % -2., // 105 % 0., // 106 % -1., // 107 % 0.5773502691896255, // 108 % -1., // 109 % 0.5773502691896255, // 110 % 0., // 111 % 0., // 112 % 1., // 113 % 0.5773502691896255, // 114 % 1., // 115 % 0.5773502691896255, // 116 % 1., // 117 % 0.5773502691896255, // 118 % 0., // 119 % 0., // 120 % ], % [ // 2 % 0., // 1 % 1.732050807568877, // 2 % 0., // 3 % 0.5773502691896255, // 4 % 1., // 5 % 1.154700538379251, // 6 % 1., // 7 % 0., // 8 % 0., // 9 % -0.5773502691896255, // 10 % 0., // 11 % 1.732050807568877, // 12 % 0., // 13 % 1.732050807568877, // 14 % 0., // 15 % 1.732050807568877, // 16 % 0., // 17 % 1.732050807568877, // 18 % 1., // 19 % 1.154700538379251, // 20 % 1., // 21 % 2.309401076758502, // 22 % 2., // 23 % 1.732050807568877, // 24 % 2., // 25 % 2.886751345948127, // 26 % 2., // 27 % 2.886751345948127, // 28 % 2., // 29 % 2.886751345948127, // 30 % 2., // 31 % 2.886751345948127, // 32 % 2., // 33 % 2.886751345948127, // 34 % 2., // 35 % 1.732050807568877, // 36 % 3., // 37 % 2.309401076758502, // 38 % 3., // 39 % 1.154700538379251, // 40 % 4., // 41 % 1.732050807568877, // 42 % 4., // 43 % 1.732050807568877, // 44 % 4., // 45 % 1.732050807568877, // 46 % 4., // 47 % 1.732050807568877, // 48 % 4., // 49 % 1.732050807568877, // 50 % 3., // 51 % 1.154700538379251, // 52 % 4., // 53 % 0.5773502691896255, // 54 % 3., // 55 % 0., // 56 % 4., // 57 % -0.5773502691896255, // 58 % 4., // 59 % -0.5773502691896255, // 60 % 4., // 61 % -0.5773502691896255, // 62 % 4., // 63 % -0.5773502691896255, // 64 % 4., // 65 % -0.5773502691896255, // 66 % 3., // 67 % 0., // 68 % 3., // 69 % -1.154700538379251, // 70 % 2., // 71 % -0.5773502691896255, // 72 % 2., // 73 % -1.732050807568877, // 74 % 2., // 75 % -1.732050807568877, // 76 % 2., // 77 % -1.732050807568877, // 78 % 2., // 79 % -1.732050807568877, // 80 % 2., // 81 % -1.732050807568877, // 82 % 2., // 83 % -0.5773502691896255, // 84 % 1., // 85 % -1.154700538379251, // 86 % 1., // 87 % 0., // 88 % 0., // 89 % -0.5773502691896255, // 90 % 1., // 91 % 1.154700538379251, // 92 % 1., // 93 % 1.154700538379251, // 94 % 2., // 95 % 1.732050807568877, // 96 % 2., // 97 % 1.732050807568877, // 98 % 3., // 99 % 1.154700538379251, // 100 % 3., // 101 % 1.154700538379251, // 102 % 3., // 103 % 0., // 104 % 3., // 105 % 0., // 106 % 2., // 107 % -0.5773502691896255, // 108 % 2., // 109 % -0.5773502691896255, // 110 % 1., // 111 % 0., // 112 % 0., // 113 % -0.5773502691896255, // 114 % 0., // 115 % -0.5773502691896255, // 116 % 0., // 117 % -0.5773502691896255, // 118 % 1., // 119 % 0., // 120 % ], % [ // 3 % 0.5773502691896255, // 1 % 2., // 2 % 0.5773502691896255, // 3 % 0.6666666666666666, // 4 % 1.732050807568877, // 5 % 1.333333333333333, // 6 % 1.732050807568877, // 7 % 0., // 8 % 0.5773502691896255, // 9 % -0.6666666666666666, // 10 % -0.5773502691896255, // 11 % 2., // 12 % 0., // 13 % 1., // 14 % -1.154700538379251, // 15 % 1., // 16 % -0.5773502691896255, // 17 % 0., // 18 % 0.5773502691896255, // 19 % -0.6666666666666666, // 20 % 0.5773502691896255, // 21 % 0.6666666666666666, // 22 % 1.732050807568877, // 23 % 0., // 24 % 1.732050807568877, // 25 % 1.333333333333333, // 26 % 1.154700538379251, // 27 % 2.333333333333333, // 28 % 0.5773502691896255, // 29 % 1.333333333333333, // 30 % 0., // 31 % 2.333333333333333, // 32 % -0.5773502691896255, // 33 % 1.333333333333333, // 34 % -0.5773502691896255, // 35 % 0., // 36 % 0.5773502691896255, // 37 % 0.6666666666666666, // 38 % 0.5773502691896255, // 39 % -0.6666666666666666, // 40 % 1.732050807568877, // 41 % 0., // 42 % 2.309401076758502, // 43 % 1., // 44 % 1.154700538379251, // 45 % 1., // 46 % 1.732050807568877, // 47 % 2., // 48 % 0.5773502691896255, // 49 % 2., // 50 % -0.5773502691896255, // 51 % 1.333333333333333, // 52 % 0.5773502691896255, // 53 % 0.6666666666666666, // 54 % -0.5773502691896255, // 55 % 0., // 56 % 0.5773502691896255, // 57 % -0.6666666666666666, // 58 % 1.732050807568877, // 59 % -0.6666666666666666, // 60 % 1.154700538379251, // 61 % 0.3333333333333333, // 62 % 2.309401076758502, // 63 % 0.3333333333333333, // 64 % 1.732050807568877, // 65 % 1.333333333333333, // 66 % 0.5773502691896255, // 67 % 2., // 68 % 0.5773502691896255, // 69 % 0.6666666666666666, // 70 % -0.5773502691896255, // 71 % 1.333333333333333, // 72 % -0.5773502691896255, // 73 % 0., // 74 % 0., // 75 % -1., // 76 % 0.5773502691896255, // 77 % 0., // 78 % 1.154700538379251, // 79 % -1., // 80 % 1.732050807568877, // 81 % 0., // 82 % 1.732050807568877, // 83 % 1.333333333333333, // 84 % 0.5773502691896255, // 85 % 0.6666666666666666, // 86 % 0.5773502691896255, // 87 % 2., // 88 % -0.5773502691896255, // 89 % 1.333333333333333, // 90 % 0.5773502691896255, // 91 % 1.333333333333333, // 92 % 0., // 93 % 0.3333333333333333, // 94 % 1.154700538379251, // 95 % 1., // 96 % 0., // 97 % 1., // 98 % 1.154700538379251, // 99 % 0.3333333333333333, // 100 % 0.5773502691896255, // 101 % 1.333333333333333, // 102 % 0.5773502691896255, // 103 % 0., // 104 % 1.154700538379251, // 105 % 1., // 106 % 0., // 107 % 0.3333333333333333, // 108 % 1.154700538379251, // 109 % 0.3333333333333333, // 110 % 0.5773502691896255, // 111 % 0., // 112 % -0.5773502691896255, // 113 % -0.6666666666666666, // 114 % 0., // 115 % 0.3333333333333333, // 116 % -1.154700538379251, // 117 % 0.3333333333333333, // 118 % 0., // 119 % 1., // 120 % ], % ]; %Vergleichsrichtung=[[1,0,0],[2,1,0]]; %Nenner=2; %DD=[ % [112,114], % [115,115], % [119,119], % [120,120], % ]; % %Beweglichkeitsgrad=1; %Einsetzkantenzahl=4; %Maxi=110; Maxj=49; MaxInvAij=42.78460969082653; //=Kante [ 56, 57 ] %gerechnet_mit_Button="acos(1/4)"; % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/6.60, 29/4.73/7.46, 30/4.73/6.46, 31/5.60/6.96, 32/5.60/5.96, 33/6.46/6.46, 34/5.96/5.60, 35/6.96/5.60, 36/6.46/4.73, 37/7.46/4.73, 38/6.60/4.23, 39/7.46/3.73, 40/6.60/3.23, 41/7.46/2.73, 42/6.46/2.73, 43/6.96/1.87, 44/5.96/1.87, 45/6.46/1.00, 46/3.23/1.87, 47/2.37/2.37, 48/1.87/3.23, 49/1.87/4.23, 50/2.37/5.10, 51/3.23/5.60, 52/4.23/5.60, 53/5.10/5.10, 54/5.60/4.23, 55/5.60/3.23, 56/4.23/1.87, 57/4.73/1.00, 58/5.60/0.50, 59/5.60/1.50, 60/5.10/2.37} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,orange!50] (p-3) -- (p-1); \draw[line width=2,orange!50] (p-3) -- (p-2); \draw[line width=2,orange!50] (p-4) -- (p-3); \draw[line width=2,orange!50] (p-4) -- (p-2); \draw[line width=2,orange!50] (p-5) -- (p-4); \draw[line width=2,orange!50] (p-5) -- (p-2); \draw[line width=2,orange!50] (p-6) -- (p-1); \draw[line width=2,orange!50] (p-7) -- (p-1); \draw[line width=2,orange!50] (p-8) -- (p-6); \draw[line width=2,orange!50] (p-9) -- (p-7); \draw[line width=2,orange!50] (p-9) -- (p-8); \draw[line width=2,orange!50] (p-10) -- (p-9); \draw[line width=2,orange!50] (p-11) -- (p-10); \draw[line width=2,orange!50] (p-12) -- (p-11); \draw[line width=2,orange!50] (p-12) -- (p-10); \draw[line width=2,orange!50] (p-13) -- (p-11); \draw[line width=2,orange!50] (p-13) -- (p-12); \draw[line width=2,orange!50] (p-14) -- (p-13); \draw[line width=2,orange!50] (p-15) -- (p-13); \draw[line width=2,orange!50] (p-15) -- (p-14); \draw[line width=2,orange!50] (p-16) -- (p-15); \draw[line width=2,orange!50] (p-16) -- (p-14); \draw[line width=2,orange!50] (p-17) -- (p-16); \draw[line width=2,orange!50] (p-18) -- (p-17); \draw[line width=2,orange!50] (p-19) -- (p-17); \draw[line width=2,orange!50] (p-19) -- (p-18); \draw[line width=2,orange!50] (p-20) -- (p-19); \draw[line width=2,orange!50] (p-20) -- (p-18); \draw[line width=2,orange!50] (p-21) -- (p-19); \draw[line width=2,orange!50] (p-21) -- (p-20); \draw[line width=2,orange!50] (p-22) -- (p-21); \draw[line width=2,orange!50] (p-23) -- (p-22); \draw[line width=2,orange!50] (p-24) -- (p-23); \draw[line width=2,orange!50] (p-24) -- (p-22); \draw[line width=2,orange!50] (p-25) -- (p-23); \draw[line width=2,orange!50] (p-25) -- (p-24); \draw[line width=2,orange!50] (p-26) -- (p-25); \draw[line width=2,orange!50] (p-27) -- (p-25); \draw[line width=2,orange!50] (p-27) -- (p-26); \draw[line width=2,orange!50] (p-28) -- (p-27); \draw[line width=2,orange!50] (p-28) -- (p-26); \draw[line width=2,orange!50] (p-29) -- (p-27); \draw[line width=2,orange!50] (p-29) -- (p-28); \draw[line width=2,orange!50] (p-30) -- (p-29); \draw[line width=2,orange!50] (p-31) -- (p-29); \draw[line width=2,orange!50] (p-32) -- (p-30); \draw[line width=2,orange!50] (p-33) -- (p-31); \draw[line width=2,orange!50] (p-33) -- (p-32); \draw[line width=2,orange!50] (p-34) -- (p-33); \draw[line width=2,orange!50] (p-35) -- (p-33); \draw[line width=2,orange!50] (p-35) -- (p-34); \draw[line width=2,orange!50] (p-36) -- (p-35); \draw[line width=2,orange!50] (p-36) -- (p-34); \draw[line width=2,orange!50] (p-37) -- (p-35); \draw[line width=2,orange!50] (p-37) -- (p-36); \draw[line width=2,orange!50] (p-38) -- (p-37); \draw[line width=2,orange!50] (p-39) -- (p-37); \draw[line width=2,orange!50] (p-39) -- (p-38); \draw[line width=2,orange!50] (p-40) -- (p-39); \draw[line width=2,orange!50] (p-40) -- (p-38); \draw[line width=2,orange!50] (p-41) -- (p-40); \draw[line width=2,orange!50] (p-42) -- (p-41); \draw[line width=2,orange!50] (p-43) -- (p-41); \draw[line width=2,orange!50] (p-43) -- (p-42); \draw[line width=2,orange!50] (p-44) -- (p-43); \draw[line width=2,orange!50] (p-44) -- (p-42); \draw[line width=2,orange!50] (p-45) -- (p-43); \draw[line width=2,orange!50] (p-45) -- (p-44); \draw[line width=2,orange!50] (p-45) -- (p-59); \draw[line width=2,orange!50] (p-46) -- (p-6); \draw[line width=2,orange!50] (p-46) -- (p-3); \draw[line width=2,orange!50] (p-46) -- (p-47); \draw[line width=2,orange!50] (p-47) -- (p-10); \draw[line width=2,orange!50] (p-47) -- (p-8); \draw[line width=2,orange!50] (p-47) -- (p-48); \draw[line width=2,orange!50] (p-48) -- (p-14); \draw[line width=2,orange!50] (p-48) -- (p-12); \draw[line width=2,orange!50] (p-50) -- (p-22); \draw[line width=2,orange!50] (p-50) -- (p-20); \draw[line width=2,orange!50] (p-50) -- (p-51); \draw[line width=2,orange!50] (p-51) -- (p-26); \draw[line width=2,orange!50] (p-51) -- (p-52); \draw[line width=2,orange!50] (p-52) -- (p-30); \draw[line width=2,orange!50] (p-52) -- (p-28); \draw[line width=2,orange!50] (p-52) -- (p-53); \draw[line width=2,orange!50] (p-53) -- (p-34); \draw[line width=2,orange!50] (p-53) -- (p-32); \draw[line width=2,orange!50] (p-53) -- (p-54); \draw[line width=2,orange!50] (p-54) -- (p-36); \draw[line width=2,orange!50] (p-54) -- (p-55); \draw[line width=2,orange!50] (p-55) -- (p-42); \draw[line width=2,orange!50] (p-55) -- (p-40); \draw[line width=2,orange!50] (p-56) -- (p-46); \draw[line width=2,orange!50] (p-56) -- (p-4); \draw[line width=2,orange!50] (p-57) -- (p-56); \draw[line width=2,orange!50] (p-57) -- (p-5); \draw[line width=2,orange!50] (p-58) -- (p-57); \draw[line width=2,orange!50] (p-58) -- (p-5); \draw[line width=2,orange!50] (p-59) -- (p-57); \draw[line width=2,orange!50] (p-59) -- (p-58); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 3 (purple): $ %Eingabe war: % %Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2); N(46,6,3); N(47,10,8); N(48,14,12); N(49,18,16); N(50,22,20); N(51,26,24); N(52,30,28); N(53,34,32); N(54,38,36); N(55,42,40); N(56,46,4); N(57,56,5); L(58,57,5); L(59,57,58); N(60,44,55); A(58,45,Bew(5)); A(45,59,Bew(6)); A(59,60,Bew(6)); A(46,47,Bew(6)); A(47,48,Bew(6)); A(48,49,Bew(6)); A(49,50,Bew(6)); A(50,51,Bew(6)); A(51,52,Bew(6)); A(52,53,Bew(6)); A(53,54,Bew(6)); A(54,55,Bew(6)); A(60,56,Bew(6)); W(); % % % % % %Belastungsarray=[ % [ // 0 % 1.732050807568877, // 1 (P1-P2) % -1.732050807568877, // 2 (P1-P3) % -0.5773502691896255, // 3 (P2-P3) % -0.5773502691896255, // 4 (P3-P4) % 0.5773502691896255, // 5 (P2-P4) % -0.5773502691896255, // 6 (P4-P5) % 1.154700538379251, // 7 (P2-P5) % 1., // 8 (P1-P6) % 1., // 9 (P1-P7) % 1., // 10 (P6-P7) % -1., // 11 (P7-P8) % 0., // 12 (P6-P8) % 2., // 13 (P7-P9) % -1., // 14 (P8-P9) % 0., // 15 (P9-P10) % 1.732050807568877, // 16 (P9-P11) % 1.154700538379251, // 17 (P10-P11) % -1.154700538379251, // 18 (P11-P12) % -0.5773502691896255, // 19 (P10-P12) % 2.886751345948127, // 20 (P11-P13) % -2.309401076758502, // 21 (P12-P13) % 1., // 22 (P13-P14) % 2., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 0., // 26 (P14-P16) % 3., // 27 (P15-P17) % -1., // 28 (P16-P17) % -0.5773502691896255, // 29 (P17-P18) % 2.886751345948127, // 30 (P17-P19) % 0.5773502691896255, // 31 (P18-P19) % -0.5773502691896255, // 32 (P19-P20) % -0.5773502691896255, // 33 (P18-P20) % 3.464101615137753, // 34 (P19-P21) % -1.732050807568877, // 35 (P20-P21) % 0., // 36 (P21-P22) % 3., // 37 (P21-P23) % 0., // 38 (P22-P23) % 0., // 39 (P23-P24) % 0., // 40 (P22-P24) % 3., // 41 (P23-P25) % 0., // 42 (P24-P25) % -1.732050807568877, // 43 (P25-P26) % 3.464101615137753, // 44 (P25-P27) % -0.5773502691896255, // 45 (P26-P27) % 0.5773502691896255, // 46 (P27-P28) % -0.5773502691896255, // 47 (P26-P28) % 2.886751345948127, // 48 (P27-P29) % -0.5773502691896255, // 49 (P28-P29) % -1., // 50 (P29-P30) % 3., // 51 (P29-P31) % -1., // 52 (P30-P31) % 1., // 53 (P31-P32) % 0., // 54 (P30-P32) % 2., // 55 (P31-P33) % 1., // 56 (P32-P33) % -2.309401076758502, // 57 (P33-P34) % 2.886751345948127, // 58 (P33-P35) % -1.154700538379251, // 59 (P34-P35) % 1.154700538379251, // 60 (P35-P36) % -0.5773502691896255, // 61 (P34-P36) % 1.732050807568877, // 62 (P35-P37) % 0., // 63 (P36-P37) % -1., // 64 (P37-P38) % 2., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 0., // 68 (P38-P40) % 1., // 69 (P39-P41) % 1., // 70 (P40-P41) % -1.732050807568877, // 71 (P41-P42) % 1.732050807568877, // 72 (P41-P43) % -0.5773502691896255, // 73 (P42-P43) % 0.5773502691896255, // 74 (P43-P44) % -0.5773502691896255, // 75 (P42-P44) % 1.154700538379251, // 76 (P43-P45) % -0.5773502691896255, // 77 (P44-P45) % 0., // 78 (P45-P59) % 1.732050807568877, // 79 (P6-P46) % -2., // 80 (P3-P46) % -1., // 81 (P46-P47) % 1., // 82 (P10-P47) % -1.732050807568877, // 83 (P8-P47) % -1.732050807568877, // 84 (P47-P48) % 1.732050807568877, // 85 (P14-P48) % -3., // 86 (P12-P48) % -3., // 87 (P48-P49) % 0., // 88 (P18-P49) % -1.732050807568877, // 89 (P16-P49) % -3.464101615137753, // 90 (P49-P50) % 0., // 91 (P22-P50) % -2., // 92 (P20-P50) % -4., // 93 (P50-P51) % -2., // 94 (P26-P51) % 0., // 95 (P24-P51) % -3.464101615137753, // 96 (P51-P52) % -1.732050807568877, // 97 (P30-P52) % 0., // 98 (P28-P52) % -3., // 99 (P52-P53) % -3., // 100 (P34-P53) % 1.732050807568877, // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % -1.732050807568877, // 103 (P38-P54) % 1., // 104 (P36-P54) % -1., // 105 (P54-P55) % -2., // 106 (P42-P55) % 1.732050807568877, // 107 (P40-P55) % 0., // 108 (P46-P56) % 0., // 109 (P4-P56) % 0., // 110 (P56-P57) % 0., // 111 (P5-P57) % 0., // 112 (P57-P58) % 1., // 113 (P5-P58) % 1., // 114 (P45-P58) % 0., // 115 (P57-P59) % 0., // 116 (P58-P59) % 0., // 117 (P59-P60) % 0., // 118 (P44-P60) % 0., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 1 % 0., // 1 (P1-P2) % -1.732050807568877, // 2 (P1-P3) % 0.5773502691896255, // 3 (P2-P3) % -1.154700538379251, // 4 (P3-P4) % -0.5773502691896255, // 5 (P2-P4) % -2.886751345948127, // 6 (P4-P5) % 0.5773502691896255, // 7 (P2-P5) % 2., // 8 (P1-P6) % -1., // 9 (P1-P7) % 0., // 10 (P6-P7) % 0., // 11 (P7-P8) % 1., // 12 (P6-P8) % -1., // 13 (P7-P9) % 2., // 14 (P8-P9) % -1.732050807568877, // 15 (P9-P10) % 0., // 16 (P9-P11) % 0.5773502691896255, // 17 (P10-P11) % -0.5773502691896255, // 18 (P11-P12) % -1.154700538379251, // 19 (P10-P12) % 0.5773502691896255, // 20 (P11-P13) % -2.886751345948127, // 21 (P12-P13) % 3., // 22 (P13-P14) % -1., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 1., // 26 (P14-P16) % 0., // 27 (P15-P17) % 1., // 28 (P16-P17) % -1.154700538379251, // 29 (P17-P18) % 0.5773502691896255, // 30 (P17-P19) % 1.154700538379251, // 31 (P18-P19) % -1.154700538379251, // 32 (P19-P20) % -1.154700538379251, // 33 (P18-P20) % 1.732050807568877, // 34 (P19-P21) % -3.464101615137753, // 35 (P20-P21) % 3., // 36 (P21-P22) % 0., // 37 (P21-P23) % 1., // 38 (P22-P23) % -1., // 39 (P23-P24) % 1., // 40 (P22-P24) % 1., // 41 (P23-P25) % 1., // 42 (P24-P25) % -1.732050807568877, // 43 (P25-P26) % 1.732050807568877, // 44 (P25-P27) % 0.5773502691896255, // 45 (P26-P27) % -0.5773502691896255, // 46 (P27-P28) % -1.154700538379251, // 47 (P26-P28) % 2.309401076758502, // 48 (P27-P29) % -2.886751345948127, // 49 (P28-P29) % 2., // 50 (P29-P30) % 1., // 51 (P29-P31) % 0., // 52 (P30-P31) % 0., // 53 (P31-P32) % 1., // 54 (P30-P32) % 1., // 55 (P31-P33) % 2., // 56 (P32-P33) % -2.886751345948127, // 57 (P33-P34) % 2.309401076758502, // 58 (P33-P35) % -0.5773502691896255, // 59 (P34-P35) % 0.5773502691896255, // 60 (P35-P36) % -1.154700538379251, // 61 (P34-P36) % 1.732050807568877, // 62 (P35-P37) % -1.732050807568877, // 63 (P36-P37) % 1., // 64 (P37-P38) % 1., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 1., // 68 (P38-P40) % 0., // 69 (P39-P41) % 3., // 70 (P40-P41) % -3.464101615137753, // 71 (P41-P42) % 1.732050807568877, // 72 (P41-P43) % -1.154700538379251, // 73 (P42-P43) % 1.154700538379251, // 74 (P43-P44) % -1.154700538379251, // 75 (P42-P44) % 0.5773502691896255, // 76 (P43-P45) % -1.154700538379251, // 77 (P44-P45) % 1., // 78 (P45-P59) % 1.732050807568877, // 79 (P6-P46) % -1., // 80 (P3-P46) % 1., // 81 (P46-P47) % -1., // 82 (P10-P47) % 1.732050807568877, // 83 (P8-P47) % 1.732050807568877, // 84 (P47-P48) % 3.464101615137753, // 85 (P14-P48) % -3., // 86 (P12-P48) % 0., // 87 (P48-P49) % 0., // 88 (P18-P49) % 0., // 89 (P16-P49) % 0., // 90 (P49-P50) % 3.464101615137753, // 91 (P22-P50) % -4., // 92 (P20-P50) % -2., // 93 (P50-P51) % -1., // 94 (P26-P51) % 0., // 95 (P24-P51) % -1.732050807568877, // 96 (P51-P52) % 1.732050807568877, // 97 (P30-P52) % -3., // 98 (P28-P52) % -3., // 99 (P52-P53) % -3., // 100 (P34-P53) % 1.732050807568877, // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % 0., // 103 (P38-P54) % -1., // 104 (P36-P54) % -2., // 105 (P54-P55) % -4., // 106 (P42-P55) % 3.464101615137753, // 107 (P40-P55) % 1.732050807568877, // 108 (P46-P56) % -3., // 109 (P4-P56) % 3.464101615137753, // 110 (P56-P57) % 3., // 111 (P5-P57) % 1., // 112 (P57-P58) % -1., // 113 (P5-P58) % 0., // 114 (P45-P58) % 1., // 115 (P57-P59) % -1., // 116 (P58-P59) % 0., // 117 (P59-P60) % 0., // 118 (P44-P60) % 0., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 2 % 2., // 1 (P1-P2) % -2., // 2 (P1-P3) % -1.333333333333333, // 3 (P2-P3) % -0.3333333333333333, // 4 (P3-P4) % 1.333333333333333, // 5 (P2-P4) % 0.6666666666666666, // 6 (P4-P5) % 0.6666666666666666, // 7 (P2-P5) % 1.154700538379251, // 8 (P1-P6) % 1.154700538379251, // 9 (P1-P7) % 1.154700538379251, // 10 (P6-P7) % -1.154700538379251, // 11 (P7-P8) % 0., // 12 (P6-P8) % 2.309401076758502, // 13 (P7-P9) % -1.154700538379251, // 14 (P8-P9) % 0., // 15 (P9-P10) % 2., // 16 (P9-P11) % 0.6666666666666666, // 17 (P10-P11) % -0.6666666666666666, // 18 (P11-P12) % -0.3333333333333333, // 19 (P10-P12) % 2.666666666666667, // 20 (P11-P13) % -1.333333333333333, // 21 (P12-P13) % 0., // 22 (P13-P14) % 2.309401076758502, // 23 (P13-P15) % 0., // 24 (P14-P15) % 0., // 25 (P15-P16) % 0., // 26 (P14-P16) % 2.309401076758502, // 27 (P15-P17) % 0., // 28 (P16-P17) % -1.333333333333333, // 29 (P17-P18) % 2.666666666666667, // 30 (P17-P19) % -0.6666666666666666, // 31 (P18-P19) % 0.6666666666666666, // 32 (P19-P20) % -0.3333333333333333, // 33 (P18-P20) % 2., // 34 (P19-P21) % 0., // 35 (P20-P21) % -1.154700538379251, // 36 (P21-P22) % 2.309401076758502, // 37 (P21-P23) % -1.154700538379251, // 38 (P22-P23) % 1.154700538379251, // 39 (P23-P24) % 0., // 40 (P22-P24) % 1.154700538379251, // 41 (P23-P25) % 1.154700538379251, // 42 (P24-P25) % -2., // 43 (P25-P26) % 2., // 44 (P25-P27) % -1.333333333333333, // 45 (P26-P27) % 1.333333333333333, // 46 (P27-P28) % -0.3333333333333333, // 47 (P26-P28) % 0.6666666666666666, // 48 (P27-P29) % 0.6666666666666666, // 49 (P28-P29) % -1.154700538379251, // 50 (P29-P30) % 1.154700538379251, // 51 (P29-P31) % -1.154700538379251, // 52 (P30-P31) % 1.154700538379251, // 53 (P31-P32) % 0., // 54 (P30-P32) % 0., // 55 (P31-P33) % 1.154700538379251, // 56 (P32-P33) % -1.333333333333333, // 57 (P33-P34) % 0.6666666666666666, // 58 (P33-P35) % -0.6666666666666666, // 59 (P34-P35) % 0.6666666666666666, // 60 (P35-P36) % -0.3333333333333333, // 61 (P34-P36) % 0., // 62 (P35-P37) % 0., // 63 (P36-P37) % 0., // 64 (P37-P38) % 0., // 65 (P37-P39) % 0., // 66 (P38-P39) % 0., // 67 (P39-P40) % 0., // 68 (P38-P40) % 0., // 69 (P39-P41) % 0., // 70 (P40-P41) % 0., // 71 (P41-P42) % 0., // 72 (P41-P43) % 0.6666666666666666, // 73 (P42-P43) % -0.6666666666666666, // 74 (P43-P44) % -0.3333333333333333, // 75 (P42-P44) % 0.6666666666666666, // 76 (P43-P45) % -1.333333333333333, // 77 (P44-P45) % 1.154700538379251, // 78 (P45-P59) % 2., // 79 (P6-P46) % -2.886751345948127, // 80 (P3-P46) % -2.309401076758502, // 81 (P46-P47) % 0.5773502691896255, // 82 (P10-P47) % -2., // 83 (P8-P47) % -3., // 84 (P47-P48) % 0., // 85 (P14-P48) % -1.732050807568877, // 86 (P12-P48) % -3.464101615137753, // 87 (P48-P49) % -1.732050807568877, // 88 (P18-P49) % 0., // 89 (P16-P49) % -3., // 90 (P49-P50) % -2., // 91 (P22-P50) % 0.5773502691896255, // 92 (P20-P50) % -2.309401076758502, // 93 (P50-P51) % -2.886751345948127, // 94 (P26-P51) % 2., // 95 (P24-P51) % -1., // 96 (P51-P52) % -2., // 97 (P30-P52) % 1.732050807568877, // 98 (P28-P52) % 0., // 99 (P52-P53) % -1.732050807568877, // 100 (P34-P53) % 2., // 101 (P32-P53) % 1., // 102 (P53-P54) % 0., // 103 (P38-P54) % 0.5773502691896255, // 104 (P36-P54) % 1.154700538379251, // 105 (P54-P55) % 0.5773502691896255, // 106 (P42-P55) % 0., // 107 (P40-P55) % -1., // 108 (P46-P56) % 1.732050807568877, // 109 (P4-P56) % -2., // 110 (P56-P57) % -1.154700538379251, // 111 (P5-P57) % -1.154700538379251, // 112 (P57-P58) % 1.154700538379251, // 113 (P5-P58) % 0., // 114 (P45-P58) % 0., // 115 (P57-P59) % 1.154700538379251, // 116 (P58-P59) % 2., // 117 (P59-P60) % -1.732050807568877, // 118 (P44-P60) % 1., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 3 % -1.154700538379251, // 1 (P1-P2) % 0.5773502691896255, // 2 (P1-P3) % 0.5773502691896255, // 3 (P2-P3) % 0., // 4 (P3-P4) % -0.5773502691896255, // 5 (P2-P4) % -0.5773502691896255, // 6 (P4-P5) % -0.5773502691896255, // 7 (P2-P5) % 0., // 8 (P1-P6) % -1., // 9 (P1-P7) % 0., // 10 (P6-P7) % 0., // 11 (P7-P8) % 0., // 12 (P6-P8) % -1., // 13 (P7-P9) % 0., // 14 (P8-P9) % 0.5773502691896255, // 15 (P9-P10) % -1.154700538379251, // 16 (P9-P11) % 0.5773502691896255, // 17 (P10-P11) % -0.5773502691896255, // 18 (P11-P12) % 0., // 19 (P10-P12) % -0.5773502691896255, // 20 (P11-P13) % -0.5773502691896255, // 21 (P12-P13) % 1., // 22 (P13-P14) % -1., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 0., // 26 (P14-P16) % 0., // 27 (P15-P17) % -1., // 28 (P16-P17) % 1.154700538379251, // 29 (P17-P18) % -0.5773502691896255, // 30 (P17-P19) % 1.154700538379251, // 31 (P18-P19) % -1.154700538379251, // 32 (P19-P20) % 0., // 33 (P18-P20) % 0.5773502691896255, // 34 (P19-P21) % -1.154700538379251, // 35 (P20-P21) % 1., // 36 (P21-P22) % 0., // 37 (P21-P23) % 1., // 38 (P22-P23) % -1., // 39 (P23-P24) % 0., // 40 (P22-P24) % 1., // 41 (P23-P25) % -1., // 42 (P24-P25) % 0.5773502691896255, // 43 (P25-P26) % 0.5773502691896255, // 44 (P25-P27) % 0.5773502691896255, // 45 (P26-P27) % -0.5773502691896255, // 46 (P27-P28) % 0., // 47 (P26-P28) % 1.154700538379251, // 48 (P27-P29) % -0.5773502691896255, // 49 (P28-P29) % 0., // 50 (P29-P30) % 1., // 51 (P29-P31) % 0., // 52 (P30-P31) % 0., // 53 (P31-P32) % 0., // 54 (P30-P32) % 1., // 55 (P31-P33) % 0., // 56 (P32-P33) % -0.5773502691896255, // 57 (P33-P34) % 1.154700538379251, // 58 (P33-P35) % -0.5773502691896255, // 59 (P34-P35) % 0.5773502691896255, // 60 (P35-P36) % 0., // 61 (P34-P36) % 0.5773502691896255, // 62 (P35-P37) % 0.5773502691896255, // 63 (P36-P37) % -1., // 64 (P37-P38) % 1., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 0., // 68 (P38-P40) % 0., // 69 (P39-P41) % 1., // 70 (P40-P41) % -1.154700538379251, // 71 (P41-P42) % 0.5773502691896255, // 72 (P41-P43) % -1.154700538379251, // 73 (P42-P43) % 1.154700538379251, // 74 (P43-P44) % 0., // 75 (P42-P44) % -0.5773502691896255, // 76 (P43-P45) % 1.154700538379251, // 77 (P44-P45) % -1., // 78 (P45-P59) % 0., // 79 (P6-P46) % 1., // 80 (P3-P46) % 2., // 81 (P46-P47) % 1., // 82 (P10-P47) % 0., // 83 (P8-P47) % 1.732050807568877, // 84 (P47-P48) % 1.732050807568877, // 85 (P14-P48) % -1., // 86 (P12-P48) % 1., // 87 (P48-P49) % 2., // 88 (P18-P49) % -1.732050807568877, // 89 (P16-P49) % 0., // 90 (P49-P50) % 1.732050807568877, // 91 (P22-P50) % -2., // 92 (P20-P50) % -1., // 93 (P50-P51) % 1., // 94 (P26-P51) % -1.732050807568877, // 95 (P24-P51) % -1.732050807568877, // 96 (P51-P52) % 0., // 97 (P30-P52) % -1., // 98 (P28-P52) % -2., // 99 (P52-P53) % -1., // 100 (P34-P53) % 0., // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % -1.732050807568877, // 103 (P38-P54) % 1., // 104 (P36-P54) % -1., // 105 (P54-P55) % -2., // 106 (P42-P55) % 1.732050807568877, // 107 (P40-P55) % 1.732050807568877, // 108 (P46-P56) % -1., // 109 (P4-P56) % 1.732050807568877, // 110 (P56-P57) % 1., // 111 (P5-P57) % 1., // 112 (P57-P58) % -1., // 113 (P5-P58) % 0., // 114 (P45-P58) % 0., // 115 (P57-P59) % -1., // 116 (P58-P59) % -1.732050807568877, // 117 (P59-P60) % 2., // 118 (P44-P60) % 0., // 119 (P55-P60) % 1., // 120 (P56-P60) % ], % ]; %Beweglichkeiten=[ % [ // 0 % -0.5773502691896255, // 1 % -1., // 2 % -0.5773502691896255, // 3 % 0.3333333333333333, // 4 % -1.732050807568877, // 5 % -0.3333333333333333, // 6 % -1.732050807568877, // 7 % 1., // 8 % -0.5773502691896255, // 9 % 1.666666666666667, // 10 % 0.5773502691896255, // 11 % -1., // 12 % 0., // 13 % 0., // 14 % 1.154700538379251, // 15 % 0., // 16 % 0.5773502691896255, // 17 % 1., // 18 % -0.5773502691896255, // 19 % 1.666666666666667, // 20 % -0.5773502691896255, // 21 % 0.3333333333333333, // 22 % -1.732050807568877, // 23 % 1., // 24 % -1.732050807568877, // 25 % -0.3333333333333333, // 26 % -1.154700538379251, // 27 % -1.333333333333333, // 28 % -0.5773502691896255, // 29 % -0.3333333333333333, // 30 % 0., // 31 % -1.333333333333333, // 32 % 0.5773502691896255, // 33 % -0.3333333333333333, // 34 % 0.5773502691896255, // 35 % 1., // 36 % -0.5773502691896255, // 37 % 0.3333333333333333, // 38 % -0.5773502691896255, // 39 % 1.666666666666667, // 40 % -1.732050807568877, // 41 % 1., // 42 % -2.309401076758502, // 43 % 0., // 44 % -1.154700538379251, // 45 % 0., // 46 % -1.732050807568877, // 47 % -1., // 48 % -0.5773502691896255, // 49 % -1., // 50 % 0.5773502691896255, // 51 % -0.3333333333333333, // 52 % -0.5773502691896255, // 53 % 0.3333333333333333, // 54 % 0.5773502691896255, // 55 % 1., // 56 % -0.5773502691896255, // 57 % 1.666666666666667, // 58 % -1.732050807568877, // 59 % 1.666666666666667, // 60 % -1.154700538379251, // 61 % 0.6666666666666666, // 62 % -2.309401076758502, // 63 % 0.6666666666666666, // 64 % -1.732050807568877, // 65 % -0.3333333333333333, // 66 % -0.5773502691896255, // 67 % -1., // 68 % -0.5773502691896255, // 69 % 0.3333333333333333, // 70 % 0.5773502691896255, // 71 % -0.3333333333333333, // 72 % 0.5773502691896255, // 73 % 1., // 74 % 0., // 75 % 2., // 76 % -0.5773502691896255, // 77 % 1., // 78 % -1.154700538379251, // 79 % 2., // 80 % -1.732050807568877, // 81 % 1., // 82 % -1.732050807568877, // 83 % -0.3333333333333333, // 84 % -0.5773502691896255, // 85 % 0.3333333333333333, // 86 % -0.5773502691896255, // 87 % -1., // 88 % 0.5773502691896255, // 89 % -0.3333333333333333, // 90 % -0.5773502691896255, // 91 % -0.3333333333333333, // 92 % 0., // 93 % 0.6666666666666666, // 94 % -1.154700538379251, // 95 % 0., // 96 % 0., // 97 % 0., // 98 % -1.154700538379251, // 99 % 0.6666666666666666, // 100 % -0.5773502691896255, // 101 % -0.3333333333333333, // 102 % -0.5773502691896255, // 103 % 1., // 104 % -1.154700538379251, // 105 % 0., // 106 % 0., // 107 % 0.6666666666666666, // 108 % -1.154700538379251, // 109 % 0.6666666666666666, // 110 % -0.5773502691896255, // 111 % 1., // 112 % 0.5773502691896255, // 113 % 1.666666666666667, // 114 % 0., // 115 % 0.6666666666666666, // 116 % 1.154700538379251, // 117 % 0.6666666666666666, // 118 % 0., // 119 % 0., // 120 % ], % [ // 1 % 1., // 1 % -1.732050807568877, // 2 % 1., // 3 % -0.5773502691896255, // 4 % 0., // 5 % -1.154700538379251, // 6 % 0., // 7 % 0., // 8 % 1., // 9 % 0.5773502691896255, // 10 % 1., // 11 % -1.732050807568877, // 12 % 1., // 13 % -1.732050807568877, // 14 % 1., // 15 % -1.732050807568877, // 16 % 1., // 17 % -1.732050807568877, // 18 % 0., // 19 % -1.154700538379251, // 20 % 0., // 21 % -2.309401076758502, // 22 % -1., // 23 % -1.732050807568877, // 24 % -1., // 25 % -2.886751345948127, // 26 % -1., // 27 % -2.886751345948127, // 28 % -1., // 29 % -2.886751345948127, // 30 % -1., // 31 % -2.886751345948127, // 32 % -1., // 33 % -2.886751345948127, // 34 % -1., // 35 % -1.732050807568877, // 36 % -2., // 37 % -2.309401076758502, // 38 % -2., // 39 % -1.154700538379251, // 40 % -3., // 41 % -1.732050807568877, // 42 % -3., // 43 % -1.732050807568877, // 44 % -3., // 45 % -1.732050807568877, // 46 % -3., // 47 % -1.732050807568877, // 48 % -3., // 49 % -1.732050807568877, // 50 % -2., // 51 % -1.154700538379251, // 52 % -3., // 53 % -0.5773502691896255, // 54 % -2., // 55 % 0., // 56 % -3., // 57 % 0.5773502691896255, // 58 % -3., // 59 % 0.5773502691896255, // 60 % -3., // 61 % 0.5773502691896255, // 62 % -3., // 63 % 0.5773502691896255, // 64 % -3., // 65 % 0.5773502691896255, // 66 % -2., // 67 % 0., // 68 % -2., // 69 % 1.154700538379251, // 70 % -1., // 71 % 0.5773502691896255, // 72 % -1., // 73 % 1.732050807568877, // 74 % -1., // 75 % 1.732050807568877, // 76 % -1., // 77 % 1.732050807568877, // 78 % -1., // 79 % 1.732050807568877, // 80 % -1., // 81 % 1.732050807568877, // 82 % -1., // 83 % 0.5773502691896255, // 84 % 0., // 85 % 1.154700538379251, // 86 % 0., // 87 % 0., // 88 % 1., // 89 % 0.5773502691896255, // 90 % 0., // 91 % -1.154700538379251, // 92 % 0., // 93 % -1.154700538379251, // 94 % -1., // 95 % -1.732050807568877, // 96 % -1., // 97 % -1.732050807568877, // 98 % -2., // 99 % -1.154700538379251, // 100 % -2., // 101 % -1.154700538379251, // 102 % -2., // 103 % 0., // 104 % -2., // 105 % 0., // 106 % -1., // 107 % 0.5773502691896255, // 108 % -1., // 109 % 0.5773502691896255, // 110 % 0., // 111 % 0., // 112 % 1., // 113 % 0.5773502691896255, // 114 % 1., // 115 % 0.5773502691896255, // 116 % 1., // 117 % 0.5773502691896255, // 118 % 0., // 119 % 0., // 120 % ], % [ // 2 % 0., // 1 % 1.732050807568877, // 2 % 0., // 3 % 0.5773502691896255, // 4 % 1., // 5 % 1.154700538379251, // 6 % 1., // 7 % 0., // 8 % 0., // 9 % -0.5773502691896255, // 10 % 0., // 11 % 1.732050807568877, // 12 % 0., // 13 % 1.732050807568877, // 14 % 0., // 15 % 1.732050807568877, // 16 % 0., // 17 % 1.732050807568877, // 18 % 1., // 19 % 1.154700538379251, // 20 % 1., // 21 % 2.309401076758502, // 22 % 2., // 23 % 1.732050807568877, // 24 % 2., // 25 % 2.886751345948127, // 26 % 2., // 27 % 2.886751345948127, // 28 % 2., // 29 % 2.886751345948127, // 30 % 2., // 31 % 2.886751345948127, // 32 % 2., // 33 % 2.886751345948127, // 34 % 2., // 35 % 1.732050807568877, // 36 % 3., // 37 % 2.309401076758502, // 38 % 3., // 39 % 1.154700538379251, // 40 % 4., // 41 % 1.732050807568877, // 42 % 4., // 43 % 1.732050807568877, // 44 % 4., // 45 % 1.732050807568877, // 46 % 4., // 47 % 1.732050807568877, // 48 % 4., // 49 % 1.732050807568877, // 50 % 3., // 51 % 1.154700538379251, // 52 % 4., // 53 % 0.5773502691896255, // 54 % 3., // 55 % 0., // 56 % 4., // 57 % -0.5773502691896255, // 58 % 4., // 59 % -0.5773502691896255, // 60 % 4., // 61 % -0.5773502691896255, // 62 % 4., // 63 % -0.5773502691896255, // 64 % 4., // 65 % -0.5773502691896255, // 66 % 3., // 67 % 0., // 68 % 3., // 69 % -1.154700538379251, // 70 % 2., // 71 % -0.5773502691896255, // 72 % 2., // 73 % -1.732050807568877, // 74 % 2., // 75 % -1.732050807568877, // 76 % 2., // 77 % -1.732050807568877, // 78 % 2., // 79 % -1.732050807568877, // 80 % 2., // 81 % -1.732050807568877, // 82 % 2., // 83 % -0.5773502691896255, // 84 % 1., // 85 % -1.154700538379251, // 86 % 1., // 87 % 0., // 88 % 0., // 89 % -0.5773502691896255, // 90 % 1., // 91 % 1.154700538379251, // 92 % 1., // 93 % 1.154700538379251, // 94 % 2., // 95 % 1.732050807568877, // 96 % 2., // 97 % 1.732050807568877, // 98 % 3., // 99 % 1.154700538379251, // 100 % 3., // 101 % 1.154700538379251, // 102 % 3., // 103 % 0., // 104 % 3., // 105 % 0., // 106 % 2., // 107 % -0.5773502691896255, // 108 % 2., // 109 % -0.5773502691896255, // 110 % 1., // 111 % 0., // 112 % 0., // 113 % -0.5773502691896255, // 114 % 0., // 115 % -0.5773502691896255, // 116 % 0., // 117 % -0.5773502691896255, // 118 % 1., // 119 % 0., // 120 % ], % [ // 3 % 0.5773502691896255, // 1 % 2., // 2 % 0.5773502691896255, // 3 % 0.6666666666666666, // 4 % 1.732050807568877, // 5 % 1.333333333333333, // 6 % 1.732050807568877, // 7 % 0., // 8 % 0.5773502691896255, // 9 % -0.6666666666666666, // 10 % -0.5773502691896255, // 11 % 2., // 12 % 0., // 13 % 1., // 14 % -1.154700538379251, // 15 % 1., // 16 % -0.5773502691896255, // 17 % 0., // 18 % 0.5773502691896255, // 19 % -0.6666666666666666, // 20 % 0.5773502691896255, // 21 % 0.6666666666666666, // 22 % 1.732050807568877, // 23 % 0., // 24 % 1.732050807568877, // 25 % 1.333333333333333, // 26 % 1.154700538379251, // 27 % 2.333333333333333, // 28 % 0.5773502691896255, // 29 % 1.333333333333333, // 30 % 0., // 31 % 2.333333333333333, // 32 % -0.5773502691896255, // 33 % 1.333333333333333, // 34 % -0.5773502691896255, // 35 % 0., // 36 % 0.5773502691896255, // 37 % 0.6666666666666666, // 38 % 0.5773502691896255, // 39 % -0.6666666666666666, // 40 % 1.732050807568877, // 41 % 0., // 42 % 2.309401076758502, // 43 % 1., // 44 % 1.154700538379251, // 45 % 1., // 46 % 1.732050807568877, // 47 % 2., // 48 % 0.5773502691896255, // 49 % 2., // 50 % -0.5773502691896255, // 51 % 1.333333333333333, // 52 % 0.5773502691896255, // 53 % 0.6666666666666666, // 54 % -0.5773502691896255, // 55 % 0., // 56 % 0.5773502691896255, // 57 % -0.6666666666666666, // 58 % 1.732050807568877, // 59 % -0.6666666666666666, // 60 % 1.154700538379251, // 61 % 0.3333333333333333, // 62 % 2.309401076758502, // 63 % 0.3333333333333333, // 64 % 1.732050807568877, // 65 % 1.333333333333333, // 66 % 0.5773502691896255, // 67 % 2., // 68 % 0.5773502691896255, // 69 % 0.6666666666666666, // 70 % -0.5773502691896255, // 71 % 1.333333333333333, // 72 % -0.5773502691896255, // 73 % 0., // 74 % 0., // 75 % -1., // 76 % 0.5773502691896255, // 77 % 0., // 78 % 1.154700538379251, // 79 % -1., // 80 % 1.732050807568877, // 81 % 0., // 82 % 1.732050807568877, // 83 % 1.333333333333333, // 84 % 0.5773502691896255, // 85 % 0.6666666666666666, // 86 % 0.5773502691896255, // 87 % 2., // 88 % -0.5773502691896255, // 89 % 1.333333333333333, // 90 % 0.5773502691896255, // 91 % 1.333333333333333, // 92 % 0., // 93 % 0.3333333333333333, // 94 % 1.154700538379251, // 95 % 1., // 96 % 0., // 97 % 1., // 98 % 1.154700538379251, // 99 % 0.3333333333333333, // 100 % 0.5773502691896255, // 101 % 1.333333333333333, // 102 % 0.5773502691896255, // 103 % 0., // 104 % 1.154700538379251, // 105 % 1., // 106 % 0., // 107 % 0.3333333333333333, // 108 % 1.154700538379251, // 109 % 0.3333333333333333, // 110 % 0.5773502691896255, // 111 % 0., // 112 % -0.5773502691896255, // 113 % -0.6666666666666666, // 114 % 0., // 115 % 0.3333333333333333, // 116 % -1.154700538379251, // 117 % 0.3333333333333333, // 118 % 0., // 119 % 1., // 120 % ], % ]; %Vergleichsrichtung=[[1,0,0],[2,1,0]]; %Nenner=2; %DD=[ % [112,114], % [115,115], % [119,119], % [120,120], % ]; % %Beweglichkeitsgrad=1; %Einsetzkantenzahl=4; %Maxi=110; Maxj=49; MaxInvAij=42.78460969082653; //=Kante [ 56, 57 ] %gerechnet_mit_Button="acos(1/4)"; % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/6.60, 29/4.73/7.46, 30/4.73/6.46, 31/5.60/6.96, 32/5.60/5.96, 33/6.46/6.46, 34/5.96/5.60, 35/6.96/5.60, 36/6.46/4.73, 37/7.46/4.73, 38/6.60/4.23, 39/7.46/3.73, 40/6.60/3.23, 41/7.46/2.73, 42/6.46/2.73, 43/6.96/1.87, 44/5.96/1.87, 45/6.46/1.00, 46/3.23/1.87, 47/2.37/2.37, 48/1.87/3.23, 49/1.87/4.23, 50/2.37/5.10, 51/3.23/5.60, 52/4.23/5.60, 53/5.10/5.10, 54/5.60/4.23, 55/5.60/3.23, 56/4.23/1.87, 57/4.73/1.00, 58/5.60/0.50, 59/5.60/1.50, 60/5.10/2.37} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,purple!50] (p-2) -- (p-1); \draw[line width=2,purple!50] (p-3) -- (p-1); \draw[line width=2,purple!50] (p-3) -- (p-2); \draw[line width=2,purple!50] (p-4) -- (p-3); \draw[line width=2,purple!50] (p-4) -- (p-2); \draw[line width=2,purple!50] (p-5) -- (p-4); \draw[line width=2,purple!50] (p-5) -- (p-2); \draw[line width=2,purple!50] (p-6) -- (p-1); \draw[line width=2,purple!50] (p-7) -- (p-1); \draw[line width=2,purple!50] (p-7) -- (p-6); \draw[line width=2,purple!50] (p-8) -- (p-7); \draw[line width=2,purple!50] (p-9) -- (p-7); \draw[line width=2,purple!50] (p-9) -- (p-8); \draw[line width=2,purple!50] (p-11) -- (p-9); \draw[line width=2,purple!50] (p-11) -- (p-10); \draw[line width=2,purple!50] (p-12) -- (p-11); \draw[line width=2,purple!50] (p-12) -- (p-10); \draw[line width=2,purple!50] (p-13) -- (p-11); \draw[line width=2,purple!50] (p-13) -- (p-12); \draw[line width=2,purple!50] (p-15) -- (p-13); \draw[line width=2,purple!50] (p-17) -- (p-15); \draw[line width=2,purple!50] (p-18) -- (p-17); \draw[line width=2,purple!50] (p-19) -- (p-17); \draw[line width=2,purple!50] (p-19) -- (p-18); \draw[line width=2,purple!50] (p-20) -- (p-19); \draw[line width=2,purple!50] (p-20) -- (p-18); \draw[line width=2,purple!50] (p-21) -- (p-19); \draw[line width=2,purple!50] (p-22) -- (p-21); \draw[line width=2,purple!50] (p-23) -- (p-21); \draw[line width=2,purple!50] (p-23) -- (p-22); \draw[line width=2,purple!50] (p-24) -- (p-23); \draw[line width=2,purple!50] (p-25) -- (p-23); \draw[line width=2,purple!50] (p-25) -- (p-24); \draw[line width=2,purple!50] (p-26) -- (p-25); \draw[line width=2,purple!50] (p-27) -- (p-25); \draw[line width=2,purple!50] (p-27) -- (p-26); \draw[line width=2,purple!50] (p-28) -- (p-27); \draw[line width=2,purple!50] (p-28) -- (p-26); \draw[line width=2,purple!50] (p-29) -- (p-27); \draw[line width=2,purple!50] (p-29) -- (p-28); \draw[line width=2,purple!50] (p-30) -- (p-29); \draw[line width=2,purple!50] (p-31) -- (p-29); \draw[line width=2,purple!50] (p-31) -- (p-30); \draw[line width=2,purple!50] (p-32) -- (p-31); \draw[line width=2,purple!50] (p-33) -- (p-32); \draw[line width=2,purple!50] (p-34) -- (p-33); \draw[line width=2,purple!50] (p-35) -- (p-33); \draw[line width=2,purple!50] (p-35) -- (p-34); \draw[line width=2,purple!50] (p-36) -- (p-35); \draw[line width=2,purple!50] (p-36) -- (p-34); \draw[line width=2,purple!50] (p-43) -- (p-42); \draw[line width=2,purple!50] (p-44) -- (p-43); \draw[line width=2,purple!50] (p-44) -- (p-42); \draw[line width=2,purple!50] (p-45) -- (p-43); \draw[line width=2,purple!50] (p-45) -- (p-44); \draw[line width=2,purple!50] (p-45) -- (p-59); \draw[line width=2,purple!50] (p-46) -- (p-6); \draw[line width=2,purple!50] (p-46) -- (p-3); \draw[line width=2,purple!50] (p-46) -- (p-47); \draw[line width=2,purple!50] (p-47) -- (p-10); \draw[line width=2,purple!50] (p-47) -- (p-8); \draw[line width=2,purple!50] (p-47) -- (p-48); \draw[line width=2,purple!50] (p-48) -- (p-12); \draw[line width=2,purple!50] (p-48) -- (p-49); \draw[line width=2,purple!50] (p-49) -- (p-18); \draw[line width=2,purple!50] (p-49) -- (p-50); \draw[line width=2,purple!50] (p-50) -- (p-22); \draw[line width=2,purple!50] (p-50) -- (p-20); \draw[line width=2,purple!50] (p-50) -- (p-51); \draw[line width=2,purple!50] (p-51) -- (p-26); \draw[line width=2,purple!50] (p-51) -- (p-24); \draw[line width=2,purple!50] (p-51) -- (p-52); \draw[line width=2,purple!50] (p-52) -- (p-30); \draw[line width=2,purple!50] (p-52) -- (p-28); \draw[line width=2,purple!50] (p-53) -- (p-34); \draw[line width=2,purple!50] (p-53) -- (p-32); \draw[line width=2,purple!50] (p-53) -- (p-54); \draw[line width=2,purple!50] (p-54) -- (p-36); \draw[line width=2,purple!50] (p-54) -- (p-55); \draw[line width=2,purple!50] (p-55) -- (p-42); \draw[line width=2,purple!50] (p-56) -- (p-46); \draw[line width=2,purple!50] (p-56) -- (p-4); \draw[line width=2,purple!50] (p-57) -- (p-56); \draw[line width=2,purple!50] (p-57) -- (p-5); \draw[line width=2,purple!50] (p-58) -- (p-57); \draw[line width=2,purple!50] (p-58) -- (p-5); \draw[line width=2,purple!50] (p-59) -- (p-58); \draw[line width=2,purple!50] (p-59) -- (p-60); \draw[line width=2,purple!50] (p-60) -- (p-44); \draw[line width=2,purple!50] (p-60) -- (p-55); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 4 (hellgrau) $ %Eingabe war: % %Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2); N(46,6,3); N(47,10,8); N(48,14,12); N(49,18,16); N(50,22,20); N(51,26,24); N(52,30,28); N(53,34,32); N(54,38,36); N(55,42,40); N(56,46,4); N(57,56,5); L(58,57,5); L(59,57,58); N(60,44,55); A(58,45,Bew(5)); A(45,59,Bew(6)); A(59,60,Bew(6)); A(46,47,Bew(6)); A(47,48,Bew(6)); A(48,49,Bew(6)); A(49,50,Bew(6)); A(50,51,Bew(6)); A(51,52,Bew(6)); A(52,53,Bew(6)); A(53,54,Bew(6)); A(54,55,Bew(6)); A(60,56,Bew(6)); W(); % % % % % %Belastungsarray=[ % [ // 0 % 1.732050807568877, // 1 (P1-P2) % -1.732050807568877, // 2 (P1-P3) % -0.5773502691896255, // 3 (P2-P3) % -0.5773502691896255, // 4 (P3-P4) % 0.5773502691896255, // 5 (P2-P4) % -0.5773502691896255, // 6 (P4-P5) % 1.154700538379251, // 7 (P2-P5) % 1., // 8 (P1-P6) % 1., // 9 (P1-P7) % 1., // 10 (P6-P7) % -1., // 11 (P7-P8) % 0., // 12 (P6-P8) % 2., // 13 (P7-P9) % -1., // 14 (P8-P9) % 0., // 15 (P9-P10) % 1.732050807568877, // 16 (P9-P11) % 1.154700538379251, // 17 (P10-P11) % -1.154700538379251, // 18 (P11-P12) % -0.5773502691896255, // 19 (P10-P12) % 2.886751345948127, // 20 (P11-P13) % -2.309401076758502, // 21 (P12-P13) % 1., // 22 (P13-P14) % 2., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 0., // 26 (P14-P16) % 3., // 27 (P15-P17) % -1., // 28 (P16-P17) % -0.5773502691896255, // 29 (P17-P18) % 2.886751345948127, // 30 (P17-P19) % 0.5773502691896255, // 31 (P18-P19) % -0.5773502691896255, // 32 (P19-P20) % -0.5773502691896255, // 33 (P18-P20) % 3.464101615137753, // 34 (P19-P21) % -1.732050807568877, // 35 (P20-P21) % 0., // 36 (P21-P22) % 3., // 37 (P21-P23) % 0., // 38 (P22-P23) % 0., // 39 (P23-P24) % 0., // 40 (P22-P24) % 3., // 41 (P23-P25) % 0., // 42 (P24-P25) % -1.732050807568877, // 43 (P25-P26) % 3.464101615137753, // 44 (P25-P27) % -0.5773502691896255, // 45 (P26-P27) % 0.5773502691896255, // 46 (P27-P28) % -0.5773502691896255, // 47 (P26-P28) % 2.886751345948127, // 48 (P27-P29) % -0.5773502691896255, // 49 (P28-P29) % -1., // 50 (P29-P30) % 3., // 51 (P29-P31) % -1., // 52 (P30-P31) % 1., // 53 (P31-P32) % 0., // 54 (P30-P32) % 2., // 55 (P31-P33) % 1., // 56 (P32-P33) % -2.309401076758502, // 57 (P33-P34) % 2.886751345948127, // 58 (P33-P35) % -1.154700538379251, // 59 (P34-P35) % 1.154700538379251, // 60 (P35-P36) % -0.5773502691896255, // 61 (P34-P36) % 1.732050807568877, // 62 (P35-P37) % 0., // 63 (P36-P37) % -1., // 64 (P37-P38) % 2., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 0., // 68 (P38-P40) % 1., // 69 (P39-P41) % 1., // 70 (P40-P41) % -1.732050807568877, // 71 (P41-P42) % 1.732050807568877, // 72 (P41-P43) % -0.5773502691896255, // 73 (P42-P43) % 0.5773502691896255, // 74 (P43-P44) % -0.5773502691896255, // 75 (P42-P44) % 1.154700538379251, // 76 (P43-P45) % -0.5773502691896255, // 77 (P44-P45) % 0., // 78 (P45-P59) % 1.732050807568877, // 79 (P6-P46) % -2., // 80 (P3-P46) % -1., // 81 (P46-P47) % 1., // 82 (P10-P47) % -1.732050807568877, // 83 (P8-P47) % -1.732050807568877, // 84 (P47-P48) % 1.732050807568877, // 85 (P14-P48) % -3., // 86 (P12-P48) % -3., // 87 (P48-P49) % 0., // 88 (P18-P49) % -1.732050807568877, // 89 (P16-P49) % -3.464101615137753, // 90 (P49-P50) % 0., // 91 (P22-P50) % -2., // 92 (P20-P50) % -4., // 93 (P50-P51) % -2., // 94 (P26-P51) % 0., // 95 (P24-P51) % -3.464101615137753, // 96 (P51-P52) % -1.732050807568877, // 97 (P30-P52) % 0., // 98 (P28-P52) % -3., // 99 (P52-P53) % -3., // 100 (P34-P53) % 1.732050807568877, // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % -1.732050807568877, // 103 (P38-P54) % 1., // 104 (P36-P54) % -1., // 105 (P54-P55) % -2., // 106 (P42-P55) % 1.732050807568877, // 107 (P40-P55) % 0., // 108 (P46-P56) % 0., // 109 (P4-P56) % 0., // 110 (P56-P57) % 0., // 111 (P5-P57) % 0., // 112 (P57-P58) % 1., // 113 (P5-P58) % 1., // 114 (P45-P58) % 0., // 115 (P57-P59) % 0., // 116 (P58-P59) % 0., // 117 (P59-P60) % 0., // 118 (P44-P60) % 0., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 1 % 0., // 1 (P1-P2) % -1.732050807568877, // 2 (P1-P3) % 0.5773502691896255, // 3 (P2-P3) % -1.154700538379251, // 4 (P3-P4) % -0.5773502691896255, // 5 (P2-P4) % -2.886751345948127, // 6 (P4-P5) % 0.5773502691896255, // 7 (P2-P5) % 2., // 8 (P1-P6) % -1., // 9 (P1-P7) % 0., // 10 (P6-P7) % 0., // 11 (P7-P8) % 1., // 12 (P6-P8) % -1., // 13 (P7-P9) % 2., // 14 (P8-P9) % -1.732050807568877, // 15 (P9-P10) % 0., // 16 (P9-P11) % 0.5773502691896255, // 17 (P10-P11) % -0.5773502691896255, // 18 (P11-P12) % -1.154700538379251, // 19 (P10-P12) % 0.5773502691896255, // 20 (P11-P13) % -2.886751345948127, // 21 (P12-P13) % 3., // 22 (P13-P14) % -1., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 1., // 26 (P14-P16) % 0., // 27 (P15-P17) % 1., // 28 (P16-P17) % -1.154700538379251, // 29 (P17-P18) % 0.5773502691896255, // 30 (P17-P19) % 1.154700538379251, // 31 (P18-P19) % -1.154700538379251, // 32 (P19-P20) % -1.154700538379251, // 33 (P18-P20) % 1.732050807568877, // 34 (P19-P21) % -3.464101615137753, // 35 (P20-P21) % 3., // 36 (P21-P22) % 0., // 37 (P21-P23) % 1., // 38 (P22-P23) % -1., // 39 (P23-P24) % 1., // 40 (P22-P24) % 1., // 41 (P23-P25) % 1., // 42 (P24-P25) % -1.732050807568877, // 43 (P25-P26) % 1.732050807568877, // 44 (P25-P27) % 0.5773502691896255, // 45 (P26-P27) % -0.5773502691896255, // 46 (P27-P28) % -1.154700538379251, // 47 (P26-P28) % 2.309401076758502, // 48 (P27-P29) % -2.886751345948127, // 49 (P28-P29) % 2., // 50 (P29-P30) % 1., // 51 (P29-P31) % 0., // 52 (P30-P31) % 0., // 53 (P31-P32) % 1., // 54 (P30-P32) % 1., // 55 (P31-P33) % 2., // 56 (P32-P33) % -2.886751345948127, // 57 (P33-P34) % 2.309401076758502, // 58 (P33-P35) % -0.5773502691896255, // 59 (P34-P35) % 0.5773502691896255, // 60 (P35-P36) % -1.154700538379251, // 61 (P34-P36) % 1.732050807568877, // 62 (P35-P37) % -1.732050807568877, // 63 (P36-P37) % 1., // 64 (P37-P38) % 1., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 1., // 68 (P38-P40) % 0., // 69 (P39-P41) % 3., // 70 (P40-P41) % -3.464101615137753, // 71 (P41-P42) % 1.732050807568877, // 72 (P41-P43) % -1.154700538379251, // 73 (P42-P43) % 1.154700538379251, // 74 (P43-P44) % -1.154700538379251, // 75 (P42-P44) % 0.5773502691896255, // 76 (P43-P45) % -1.154700538379251, // 77 (P44-P45) % 1., // 78 (P45-P59) % 1.732050807568877, // 79 (P6-P46) % -1., // 80 (P3-P46) % 1., // 81 (P46-P47) % -1., // 82 (P10-P47) % 1.732050807568877, // 83 (P8-P47) % 1.732050807568877, // 84 (P47-P48) % 3.464101615137753, // 85 (P14-P48) % -3., // 86 (P12-P48) % 0., // 87 (P48-P49) % 0., // 88 (P18-P49) % 0., // 89 (P16-P49) % 0., // 90 (P49-P50) % 3.464101615137753, // 91 (P22-P50) % -4., // 92 (P20-P50) % -2., // 93 (P50-P51) % -1., // 94 (P26-P51) % 0., // 95 (P24-P51) % -1.732050807568877, // 96 (P51-P52) % 1.732050807568877, // 97 (P30-P52) % -3., // 98 (P28-P52) % -3., // 99 (P52-P53) % -3., // 100 (P34-P53) % 1.732050807568877, // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % 0., // 103 (P38-P54) % -1., // 104 (P36-P54) % -2., // 105 (P54-P55) % -4., // 106 (P42-P55) % 3.464101615137753, // 107 (P40-P55) % 1.732050807568877, // 108 (P46-P56) % -3., // 109 (P4-P56) % 3.464101615137753, // 110 (P56-P57) % 3., // 111 (P5-P57) % 1., // 112 (P57-P58) % -1., // 113 (P5-P58) % 0., // 114 (P45-P58) % 1., // 115 (P57-P59) % -1., // 116 (P58-P59) % 0., // 117 (P59-P60) % 0., // 118 (P44-P60) % 0., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 2 % 2., // 1 (P1-P2) % -2., // 2 (P1-P3) % -1.333333333333333, // 3 (P2-P3) % -0.3333333333333333, // 4 (P3-P4) % 1.333333333333333, // 5 (P2-P4) % 0.6666666666666666, // 6 (P4-P5) % 0.6666666666666666, // 7 (P2-P5) % 1.154700538379251, // 8 (P1-P6) % 1.154700538379251, // 9 (P1-P7) % 1.154700538379251, // 10 (P6-P7) % -1.154700538379251, // 11 (P7-P8) % 0., // 12 (P6-P8) % 2.309401076758502, // 13 (P7-P9) % -1.154700538379251, // 14 (P8-P9) % 0., // 15 (P9-P10) % 2., // 16 (P9-P11) % 0.6666666666666666, // 17 (P10-P11) % -0.6666666666666666, // 18 (P11-P12) % -0.3333333333333333, // 19 (P10-P12) % 2.666666666666667, // 20 (P11-P13) % -1.333333333333333, // 21 (P12-P13) % 0., // 22 (P13-P14) % 2.309401076758502, // 23 (P13-P15) % 0., // 24 (P14-P15) % 0., // 25 (P15-P16) % 0., // 26 (P14-P16) % 2.309401076758502, // 27 (P15-P17) % 0., // 28 (P16-P17) % -1.333333333333333, // 29 (P17-P18) % 2.666666666666667, // 30 (P17-P19) % -0.6666666666666666, // 31 (P18-P19) % 0.6666666666666666, // 32 (P19-P20) % -0.3333333333333333, // 33 (P18-P20) % 2., // 34 (P19-P21) % 0., // 35 (P20-P21) % -1.154700538379251, // 36 (P21-P22) % 2.309401076758502, // 37 (P21-P23) % -1.154700538379251, // 38 (P22-P23) % 1.154700538379251, // 39 (P23-P24) % 0., // 40 (P22-P24) % 1.154700538379251, // 41 (P23-P25) % 1.154700538379251, // 42 (P24-P25) % -2., // 43 (P25-P26) % 2., // 44 (P25-P27) % -1.333333333333333, // 45 (P26-P27) % 1.333333333333333, // 46 (P27-P28) % -0.3333333333333333, // 47 (P26-P28) % 0.6666666666666666, // 48 (P27-P29) % 0.6666666666666666, // 49 (P28-P29) % -1.154700538379251, // 50 (P29-P30) % 1.154700538379251, // 51 (P29-P31) % -1.154700538379251, // 52 (P30-P31) % 1.154700538379251, // 53 (P31-P32) % 0., // 54 (P30-P32) % 0., // 55 (P31-P33) % 1.154700538379251, // 56 (P32-P33) % -1.333333333333333, // 57 (P33-P34) % 0.6666666666666666, // 58 (P33-P35) % -0.6666666666666666, // 59 (P34-P35) % 0.6666666666666666, // 60 (P35-P36) % -0.3333333333333333, // 61 (P34-P36) % 0., // 62 (P35-P37) % 0., // 63 (P36-P37) % 0., // 64 (P37-P38) % 0., // 65 (P37-P39) % 0., // 66 (P38-P39) % 0., // 67 (P39-P40) % 0., // 68 (P38-P40) % 0., // 69 (P39-P41) % 0., // 70 (P40-P41) % 0., // 71 (P41-P42) % 0., // 72 (P41-P43) % 0.6666666666666666, // 73 (P42-P43) % -0.6666666666666666, // 74 (P43-P44) % -0.3333333333333333, // 75 (P42-P44) % 0.6666666666666666, // 76 (P43-P45) % -1.333333333333333, // 77 (P44-P45) % 1.154700538379251, // 78 (P45-P59) % 2., // 79 (P6-P46) % -2.886751345948127, // 80 (P3-P46) % -2.309401076758502, // 81 (P46-P47) % 0.5773502691896255, // 82 (P10-P47) % -2., // 83 (P8-P47) % -3., // 84 (P47-P48) % 0., // 85 (P14-P48) % -1.732050807568877, // 86 (P12-P48) % -3.464101615137753, // 87 (P48-P49) % -1.732050807568877, // 88 (P18-P49) % 0., // 89 (P16-P49) % -3., // 90 (P49-P50) % -2., // 91 (P22-P50) % 0.5773502691896255, // 92 (P20-P50) % -2.309401076758502, // 93 (P50-P51) % -2.886751345948127, // 94 (P26-P51) % 2., // 95 (P24-P51) % -1., // 96 (P51-P52) % -2., // 97 (P30-P52) % 1.732050807568877, // 98 (P28-P52) % 0., // 99 (P52-P53) % -1.732050807568877, // 100 (P34-P53) % 2., // 101 (P32-P53) % 1., // 102 (P53-P54) % 0., // 103 (P38-P54) % 0.5773502691896255, // 104 (P36-P54) % 1.154700538379251, // 105 (P54-P55) % 0.5773502691896255, // 106 (P42-P55) % 0., // 107 (P40-P55) % -1., // 108 (P46-P56) % 1.732050807568877, // 109 (P4-P56) % -2., // 110 (P56-P57) % -1.154700538379251, // 111 (P5-P57) % -1.154700538379251, // 112 (P57-P58) % 1.154700538379251, // 113 (P5-P58) % 0., // 114 (P45-P58) % 0., // 115 (P57-P59) % 1.154700538379251, // 116 (P58-P59) % 2., // 117 (P59-P60) % -1.732050807568877, // 118 (P44-P60) % 1., // 119 (P55-P60) % 0., // 120 (P56-P60) % ], % [ // 3 % -1.154700538379251, // 1 (P1-P2) % 0.5773502691896255, // 2 (P1-P3) % 0.5773502691896255, // 3 (P2-P3) % 0., // 4 (P3-P4) % -0.5773502691896255, // 5 (P2-P4) % -0.5773502691896255, // 6 (P4-P5) % -0.5773502691896255, // 7 (P2-P5) % 0., // 8 (P1-P6) % -1., // 9 (P1-P7) % 0., // 10 (P6-P7) % 0., // 11 (P7-P8) % 0., // 12 (P6-P8) % -1., // 13 (P7-P9) % 0., // 14 (P8-P9) % 0.5773502691896255, // 15 (P9-P10) % -1.154700538379251, // 16 (P9-P11) % 0.5773502691896255, // 17 (P10-P11) % -0.5773502691896255, // 18 (P11-P12) % 0., // 19 (P10-P12) % -0.5773502691896255, // 20 (P11-P13) % -0.5773502691896255, // 21 (P12-P13) % 1., // 22 (P13-P14) % -1., // 23 (P13-P15) % 1., // 24 (P14-P15) % -1., // 25 (P15-P16) % 0., // 26 (P14-P16) % 0., // 27 (P15-P17) % -1., // 28 (P16-P17) % 1.154700538379251, // 29 (P17-P18) % -0.5773502691896255, // 30 (P17-P19) % 1.154700538379251, // 31 (P18-P19) % -1.154700538379251, // 32 (P19-P20) % 0., // 33 (P18-P20) % 0.5773502691896255, // 34 (P19-P21) % -1.154700538379251, // 35 (P20-P21) % 1., // 36 (P21-P22) % 0., // 37 (P21-P23) % 1., // 38 (P22-P23) % -1., // 39 (P23-P24) % 0., // 40 (P22-P24) % 1., // 41 (P23-P25) % -1., // 42 (P24-P25) % 0.5773502691896255, // 43 (P25-P26) % 0.5773502691896255, // 44 (P25-P27) % 0.5773502691896255, // 45 (P26-P27) % -0.5773502691896255, // 46 (P27-P28) % 0., // 47 (P26-P28) % 1.154700538379251, // 48 (P27-P29) % -0.5773502691896255, // 49 (P28-P29) % 0., // 50 (P29-P30) % 1., // 51 (P29-P31) % 0., // 52 (P30-P31) % 0., // 53 (P31-P32) % 0., // 54 (P30-P32) % 1., // 55 (P31-P33) % 0., // 56 (P32-P33) % -0.5773502691896255, // 57 (P33-P34) % 1.154700538379251, // 58 (P33-P35) % -0.5773502691896255, // 59 (P34-P35) % 0.5773502691896255, // 60 (P35-P36) % 0., // 61 (P34-P36) % 0.5773502691896255, // 62 (P35-P37) % 0.5773502691896255, // 63 (P36-P37) % -1., // 64 (P37-P38) % 1., // 65 (P37-P39) % -1., // 66 (P38-P39) % 1., // 67 (P39-P40) % 0., // 68 (P38-P40) % 0., // 69 (P39-P41) % 1., // 70 (P40-P41) % -1.154700538379251, // 71 (P41-P42) % 0.5773502691896255, // 72 (P41-P43) % -1.154700538379251, // 73 (P42-P43) % 1.154700538379251, // 74 (P43-P44) % 0., // 75 (P42-P44) % -0.5773502691896255, // 76 (P43-P45) % 1.154700538379251, // 77 (P44-P45) % -1., // 78 (P45-P59) % 0., // 79 (P6-P46) % 1., // 80 (P3-P46) % 2., // 81 (P46-P47) % 1., // 82 (P10-P47) % 0., // 83 (P8-P47) % 1.732050807568877, // 84 (P47-P48) % 1.732050807568877, // 85 (P14-P48) % -1., // 86 (P12-P48) % 1., // 87 (P48-P49) % 2., // 88 (P18-P49) % -1.732050807568877, // 89 (P16-P49) % 0., // 90 (P49-P50) % 1.732050807568877, // 91 (P22-P50) % -2., // 92 (P20-P50) % -1., // 93 (P50-P51) % 1., // 94 (P26-P51) % -1.732050807568877, // 95 (P24-P51) % -1.732050807568877, // 96 (P51-P52) % 0., // 97 (P30-P52) % -1., // 98 (P28-P52) % -2., // 99 (P52-P53) % -1., // 100 (P34-P53) % 0., // 101 (P32-P53) % -1.732050807568877, // 102 (P53-P54) % -1.732050807568877, // 103 (P38-P54) % 1., // 104 (P36-P54) % -1., // 105 (P54-P55) % -2., // 106 (P42-P55) % 1.732050807568877, // 107 (P40-P55) % 1.732050807568877, // 108 (P46-P56) % -1., // 109 (P4-P56) % 1.732050807568877, // 110 (P56-P57) % 1., // 111 (P5-P57) % 1., // 112 (P57-P58) % -1., // 113 (P5-P58) % 0., // 114 (P45-P58) % 0., // 115 (P57-P59) % -1., // 116 (P58-P59) % -1.732050807568877, // 117 (P59-P60) % 2., // 118 (P44-P60) % 0., // 119 (P55-P60) % 1., // 120 (P56-P60) % ], % ]; %Beweglichkeiten=[ % [ // 0 % -0.5773502691896255, // 1 % -1., // 2 % -0.5773502691896255, // 3 % 0.3333333333333333, // 4 % -1.732050807568877, // 5 % -0.3333333333333333, // 6 % -1.732050807568877, // 7 % 1., // 8 % -0.5773502691896255, // 9 % 1.666666666666667, // 10 % 0.5773502691896255, // 11 % -1., // 12 % 0., // 13 % 0., // 14 % 1.154700538379251, // 15 % 0., // 16 % 0.5773502691896255, // 17 % 1., // 18 % -0.5773502691896255, // 19 % 1.666666666666667, // 20 % -0.5773502691896255, // 21 % 0.3333333333333333, // 22 % -1.732050807568877, // 23 % 1., // 24 % -1.732050807568877, // 25 % -0.3333333333333333, // 26 % -1.154700538379251, // 27 % -1.333333333333333, // 28 % -0.5773502691896255, // 29 % -0.3333333333333333, // 30 % 0., // 31 % -1.333333333333333, // 32 % 0.5773502691896255, // 33 % -0.3333333333333333, // 34 % 0.5773502691896255, // 35 % 1., // 36 % -0.5773502691896255, // 37 % 0.3333333333333333, // 38 % -0.5773502691896255, // 39 % 1.666666666666667, // 40 % -1.732050807568877, // 41 % 1., // 42 % -2.309401076758502, // 43 % 0., // 44 % -1.154700538379251, // 45 % 0., // 46 % -1.732050807568877, // 47 % -1., // 48 % -0.5773502691896255, // 49 % -1., // 50 % 0.5773502691896255, // 51 % -0.3333333333333333, // 52 % -0.5773502691896255, // 53 % 0.3333333333333333, // 54 % 0.5773502691896255, // 55 % 1., // 56 % -0.5773502691896255, // 57 % 1.666666666666667, // 58 % -1.732050807568877, // 59 % 1.666666666666667, // 60 % -1.154700538379251, // 61 % 0.6666666666666666, // 62 % -2.309401076758502, // 63 % 0.6666666666666666, // 64 % -1.732050807568877, // 65 % -0.3333333333333333, // 66 % -0.5773502691896255, // 67 % -1., // 68 % -0.5773502691896255, // 69 % 0.3333333333333333, // 70 % 0.5773502691896255, // 71 % -0.3333333333333333, // 72 % 0.5773502691896255, // 73 % 1., // 74 % 0., // 75 % 2., // 76 % -0.5773502691896255, // 77 % 1., // 78 % -1.154700538379251, // 79 % 2., // 80 % -1.732050807568877, // 81 % 1., // 82 % -1.732050807568877, // 83 % -0.3333333333333333, // 84 % -0.5773502691896255, // 85 % 0.3333333333333333, // 86 % -0.5773502691896255, // 87 % -1., // 88 % 0.5773502691896255, // 89 % -0.3333333333333333, // 90 % -0.5773502691896255, // 91 % -0.3333333333333333, // 92 % 0., // 93 % 0.6666666666666666, // 94 % -1.154700538379251, // 95 % 0., // 96 % 0., // 97 % 0., // 98 % -1.154700538379251, // 99 % 0.6666666666666666, // 100 % -0.5773502691896255, // 101 % -0.3333333333333333, // 102 % -0.5773502691896255, // 103 % 1., // 104 % -1.154700538379251, // 105 % 0., // 106 % 0., // 107 % 0.6666666666666666, // 108 % -1.154700538379251, // 109 % 0.6666666666666666, // 110 % -0.5773502691896255, // 111 % 1., // 112 % 0.5773502691896255, // 113 % 1.666666666666667, // 114 % 0., // 115 % 0.6666666666666666, // 116 % 1.154700538379251, // 117 % 0.6666666666666666, // 118 % 0., // 119 % 0., // 120 % ], % [ // 1 % 1., // 1 % -1.732050807568877, // 2 % 1., // 3 % -0.5773502691896255, // 4 % 0., // 5 % -1.154700538379251, // 6 % 0., // 7 % 0., // 8 % 1., // 9 % 0.5773502691896255, // 10 % 1., // 11 % -1.732050807568877, // 12 % 1., // 13 % -1.732050807568877, // 14 % 1., // 15 % -1.732050807568877, // 16 % 1., // 17 % -1.732050807568877, // 18 % 0., // 19 % -1.154700538379251, // 20 % 0., // 21 % -2.309401076758502, // 22 % -1., // 23 % -1.732050807568877, // 24 % -1., // 25 % -2.886751345948127, // 26 % -1., // 27 % -2.886751345948127, // 28 % -1., // 29 % -2.886751345948127, // 30 % -1., // 31 % -2.886751345948127, // 32 % -1., // 33 % -2.886751345948127, // 34 % -1., // 35 % -1.732050807568877, // 36 % -2., // 37 % -2.309401076758502, // 38 % -2., // 39 % -1.154700538379251, // 40 % -3., // 41 % -1.732050807568877, // 42 % -3., // 43 % -1.732050807568877, // 44 % -3., // 45 % -1.732050807568877, // 46 % -3., // 47 % -1.732050807568877, // 48 % -3., // 49 % -1.732050807568877, // 50 % -2., // 51 % -1.154700538379251, // 52 % -3., // 53 % -0.5773502691896255, // 54 % -2., // 55 % 0., // 56 % -3., // 57 % 0.5773502691896255, // 58 % -3., // 59 % 0.5773502691896255, // 60 % -3., // 61 % 0.5773502691896255, // 62 % -3., // 63 % 0.5773502691896255, // 64 % -3., // 65 % 0.5773502691896255, // 66 % -2., // 67 % 0., // 68 % -2., // 69 % 1.154700538379251, // 70 % -1., // 71 % 0.5773502691896255, // 72 % -1., // 73 % 1.732050807568877, // 74 % -1., // 75 % 1.732050807568877, // 76 % -1., // 77 % 1.732050807568877, // 78 % -1., // 79 % 1.732050807568877, // 80 % -1., // 81 % 1.732050807568877, // 82 % -1., // 83 % 0.5773502691896255, // 84 % 0., // 85 % 1.154700538379251, // 86 % 0., // 87 % 0., // 88 % 1., // 89 % 0.5773502691896255, // 90 % 0., // 91 % -1.154700538379251, // 92 % 0., // 93 % -1.154700538379251, // 94 % -1., // 95 % -1.732050807568877, // 96 % -1., // 97 % -1.732050807568877, // 98 % -2., // 99 % -1.154700538379251, // 100 % -2., // 101 % -1.154700538379251, // 102 % -2., // 103 % 0., // 104 % -2., // 105 % 0., // 106 % -1., // 107 % 0.5773502691896255, // 108 % -1., // 109 % 0.5773502691896255, // 110 % 0., // 111 % 0., // 112 % 1., // 113 % 0.5773502691896255, // 114 % 1., // 115 % 0.5773502691896255, // 116 % 1., // 117 % 0.5773502691896255, // 118 % 0., // 119 % 0., // 120 % ], % [ // 2 % 0., // 1 % 1.732050807568877, // 2 % 0., // 3 % 0.5773502691896255, // 4 % 1., // 5 % 1.154700538379251, // 6 % 1., // 7 % 0., // 8 % 0., // 9 % -0.5773502691896255, // 10 % 0., // 11 % 1.732050807568877, // 12 % 0., // 13 % 1.732050807568877, // 14 % 0., // 15 % 1.732050807568877, // 16 % 0., // 17 % 1.732050807568877, // 18 % 1., // 19 % 1.154700538379251, // 20 % 1., // 21 % 2.309401076758502, // 22 % 2., // 23 % 1.732050807568877, // 24 % 2., // 25 % 2.886751345948127, // 26 % 2., // 27 % 2.886751345948127, // 28 % 2., // 29 % 2.886751345948127, // 30 % 2., // 31 % 2.886751345948127, // 32 % 2., // 33 % 2.886751345948127, // 34 % 2., // 35 % 1.732050807568877, // 36 % 3., // 37 % 2.309401076758502, // 38 % 3., // 39 % 1.154700538379251, // 40 % 4., // 41 % 1.732050807568877, // 42 % 4., // 43 % 1.732050807568877, // 44 % 4., // 45 % 1.732050807568877, // 46 % 4., // 47 % 1.732050807568877, // 48 % 4., // 49 % 1.732050807568877, // 50 % 3., // 51 % 1.154700538379251, // 52 % 4., // 53 % 0.5773502691896255, // 54 % 3., // 55 % 0., // 56 % 4., // 57 % -0.5773502691896255, // 58 % 4., // 59 % -0.5773502691896255, // 60 % 4., // 61 % -0.5773502691896255, // 62 % 4., // 63 % -0.5773502691896255, // 64 % 4., // 65 % -0.5773502691896255, // 66 % 3., // 67 % 0., // 68 % 3., // 69 % -1.154700538379251, // 70 % 2., // 71 % -0.5773502691896255, // 72 % 2., // 73 % -1.732050807568877, // 74 % 2., // 75 % -1.732050807568877, // 76 % 2., // 77 % -1.732050807568877, // 78 % 2., // 79 % -1.732050807568877, // 80 % 2., // 81 % -1.732050807568877, // 82 % 2., // 83 % -0.5773502691896255, // 84 % 1., // 85 % -1.154700538379251, // 86 % 1., // 87 % 0., // 88 % 0., // 89 % -0.5773502691896255, // 90 % 1., // 91 % 1.154700538379251, // 92 % 1., // 93 % 1.154700538379251, // 94 % 2., // 95 % 1.732050807568877, // 96 % 2., // 97 % 1.732050807568877, // 98 % 3., // 99 % 1.154700538379251, // 100 % 3., // 101 % 1.154700538379251, // 102 % 3., // 103 % 0., // 104 % 3., // 105 % 0., // 106 % 2., // 107 % -0.5773502691896255, // 108 % 2., // 109 % -0.5773502691896255, // 110 % 1., // 111 % 0., // 112 % 0., // 113 % -0.5773502691896255, // 114 % 0., // 115 % -0.5773502691896255, // 116 % 0., // 117 % -0.5773502691896255, // 118 % 1., // 119 % 0., // 120 % ], % [ // 3 % 0.5773502691896255, // 1 % 2., // 2 % 0.5773502691896255, // 3 % 0.6666666666666666, // 4 % 1.732050807568877, // 5 % 1.333333333333333, // 6 % 1.732050807568877, // 7 % 0., // 8 % 0.5773502691896255, // 9 % -0.6666666666666666, // 10 % -0.5773502691896255, // 11 % 2., // 12 % 0., // 13 % 1., // 14 % -1.154700538379251, // 15 % 1., // 16 % -0.5773502691896255, // 17 % 0., // 18 % 0.5773502691896255, // 19 % -0.6666666666666666, // 20 % 0.5773502691896255, // 21 % 0.6666666666666666, // 22 % 1.732050807568877, // 23 % 0., // 24 % 1.732050807568877, // 25 % 1.333333333333333, // 26 % 1.154700538379251, // 27 % 2.333333333333333, // 28 % 0.5773502691896255, // 29 % 1.333333333333333, // 30 % 0., // 31 % 2.333333333333333, // 32 % -0.5773502691896255, // 33 % 1.333333333333333, // 34 % -0.5773502691896255, // 35 % 0., // 36 % 0.5773502691896255, // 37 % 0.6666666666666666, // 38 % 0.5773502691896255, // 39 % -0.6666666666666666, // 40 % 1.732050807568877, // 41 % 0., // 42 % 2.309401076758502, // 43 % 1., // 44 % 1.154700538379251, // 45 % 1., // 46 % 1.732050807568877, // 47 % 2., // 48 % 0.5773502691896255, // 49 % 2., // 50 % -0.5773502691896255, // 51 % 1.333333333333333, // 52 % 0.5773502691896255, // 53 % 0.6666666666666666, // 54 % -0.5773502691896255, // 55 % 0., // 56 % 0.5773502691896255, // 57 % -0.6666666666666666, // 58 % 1.732050807568877, // 59 % -0.6666666666666666, // 60 % 1.154700538379251, // 61 % 0.3333333333333333, // 62 % 2.309401076758502, // 63 % 0.3333333333333333, // 64 % 1.732050807568877, // 65 % 1.333333333333333, // 66 % 0.5773502691896255, // 67 % 2., // 68 % 0.5773502691896255, // 69 % 0.6666666666666666, // 70 % -0.5773502691896255, // 71 % 1.333333333333333, // 72 % -0.5773502691896255, // 73 % 0., // 74 % 0., // 75 % -1., // 76 % 0.5773502691896255, // 77 % 0., // 78 % 1.154700538379251, // 79 % -1., // 80 % 1.732050807568877, // 81 % 0., // 82 % 1.732050807568877, // 83 % 1.333333333333333, // 84 % 0.5773502691896255, // 85 % 0.6666666666666666, // 86 % 0.5773502691896255, // 87 % 2., // 88 % -0.5773502691896255, // 89 % 1.333333333333333, // 90 % 0.5773502691896255, // 91 % 1.333333333333333, // 92 % 0., // 93 % 0.3333333333333333, // 94 % 1.154700538379251, // 95 % 1., // 96 % 0., // 97 % 1., // 98 % 1.154700538379251, // 99 % 0.3333333333333333, // 100 % 0.5773502691896255, // 101 % 1.333333333333333, // 102 % 0.5773502691896255, // 103 % 0., // 104 % 1.154700538379251, // 105 % 1., // 106 % 0., // 107 % 0.3333333333333333, // 108 % 1.154700538379251, // 109 % 0.3333333333333333, // 110 % 0.5773502691896255, // 111 % 0., // 112 % -0.5773502691896255, // 113 % -0.6666666666666666, // 114 % 0., // 115 % 0.3333333333333333, // 116 % -1.154700538379251, // 117 % 0.3333333333333333, // 118 % 0., // 119 % 1., // 120 % ], % ]; %Vergleichsrichtung=[[1,0,0],[2,1,0]]; %Nenner=2; %DD=[ % [112,114], % [115,115], % [119,119], % [120,120], % ]; % %Beweglichkeitsgrad=1; %Einsetzkantenzahl=4; %Maxi=110; Maxj=49; MaxInvAij=42.78460969082653; //=Kante [ 56, 57 ] %gerechnet_mit_Button="acos(1/4)"; % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/6.60, 29/4.73/7.46, 30/4.73/6.46, 31/5.60/6.96, 32/5.60/5.96, 33/6.46/6.46, 34/5.96/5.60, 35/6.96/5.60, 36/6.46/4.73, 37/7.46/4.73, 38/6.60/4.23, 39/7.46/3.73, 40/6.60/3.23, 41/7.46/2.73, 42/6.46/2.73, 43/6.96/1.87, 44/5.96/1.87, 45/6.46/1.00, 46/3.23/1.87, 47/2.37/2.37, 48/1.87/3.23, 49/1.87/4.23, 50/2.37/5.10, 51/3.23/5.60, 52/4.23/5.60, 53/5.10/5.10, 54/5.60/4.23, 55/5.60/3.23, 56/4.23/1.87, 57/4.73/1.00, 58/5.60/0.50, 59/5.60/1.50, 60/5.10/2.37} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,darkgray!50] (p-2) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-2); \draw[line width=2,darkgray!50] (p-4) -- (p-2); \draw[line width=2,darkgray!50] (p-5) -- (p-4); \draw[line width=2,darkgray!50] (p-5) -- (p-2); \draw[line width=2,darkgray!50] (p-7) -- (p-1); \draw[line width=2,darkgray!50] (p-9) -- (p-7); \draw[line width=2,darkgray!50] (p-10) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-10); \draw[line width=2,darkgray!50] (p-12) -- (p-11); \draw[line width=2,darkgray!50] (p-13) -- (p-11); \draw[line width=2,darkgray!50] (p-13) -- (p-12); \draw[line width=2,darkgray!50] (p-14) -- (p-13); \draw[line width=2,darkgray!50] (p-15) -- (p-13); \draw[line width=2,darkgray!50] (p-15) -- (p-14); \draw[line width=2,darkgray!50] (p-16) -- (p-15); \draw[line width=2,darkgray!50] (p-17) -- (p-16); \draw[line width=2,darkgray!50] (p-18) -- (p-17); \draw[line width=2,darkgray!50] (p-19) -- (p-17); \draw[line width=2,darkgray!50] (p-19) -- (p-18); \draw[line width=2,darkgray!50] (p-20) -- (p-19); \draw[line width=2,darkgray!50] (p-21) -- (p-19); \draw[line width=2,darkgray!50] (p-21) -- (p-20); \draw[line width=2,darkgray!50] (p-22) -- (p-21); \draw[line width=2,darkgray!50] (p-23) -- (p-22); \draw[line width=2,darkgray!50] (p-24) -- (p-23); \draw[line width=2,darkgray!50] (p-25) -- (p-23); \draw[line width=2,darkgray!50] (p-25) -- (p-24); \draw[line width=2,darkgray!50] (p-26) -- (p-25); \draw[line width=2,darkgray!50] (p-27) -- (p-25); \draw[line width=2,darkgray!50] (p-27) -- (p-26); \draw[line width=2,darkgray!50] (p-28) -- (p-27); \draw[line width=2,darkgray!50] (p-29) -- (p-27); \draw[line width=2,darkgray!50] (p-29) -- (p-28); \draw[line width=2,darkgray!50] (p-31) -- (p-29); \draw[line width=2,darkgray!50] (p-33) -- (p-31); \draw[line width=2,darkgray!50] (p-34) -- (p-33); \draw[line width=2,darkgray!50] (p-35) -- (p-33); \draw[line width=2,darkgray!50] (p-35) -- (p-34); \draw[line width=2,darkgray!50] (p-36) -- (p-35); \draw[line width=2,darkgray!50] (p-37) -- (p-35); \draw[line width=2,darkgray!50] (p-37) -- (p-36); \draw[line width=2,darkgray!50] (p-38) -- (p-37); \draw[line width=2,darkgray!50] (p-39) -- (p-37); \draw[line width=2,darkgray!50] (p-39) -- (p-38); \draw[line width=2,darkgray!50] (p-40) -- (p-39); \draw[line width=2,darkgray!50] (p-41) -- (p-40); \draw[line width=2,darkgray!50] (p-42) -- (p-41); \draw[line width=2,darkgray!50] (p-43) -- (p-41); \draw[line width=2,darkgray!50] (p-43) -- (p-42); \draw[line width=2,darkgray!50] (p-44) -- (p-43); \draw[line width=2,darkgray!50] (p-45) -- (p-43); \draw[line width=2,darkgray!50] (p-45) -- (p-44); \draw[line width=2,darkgray!50] (p-45) -- (p-59); \draw[line width=2,darkgray!50] (p-46) -- (p-3); \draw[line width=2,darkgray!50] (p-46) -- (p-47); \draw[line width=2,darkgray!50] (p-47) -- (p-10); \draw[line width=2,darkgray!50] (p-47) -- (p-48); \draw[line width=2,darkgray!50] (p-48) -- (p-14); \draw[line width=2,darkgray!50] (p-48) -- (p-12); \draw[line width=2,darkgray!50] (p-48) -- (p-49); \draw[line width=2,darkgray!50] (p-49) -- (p-18); \draw[line width=2,darkgray!50] (p-49) -- (p-16); \draw[line width=2,darkgray!50] (p-50) -- (p-22); \draw[line width=2,darkgray!50] (p-50) -- (p-20); \draw[line width=2,darkgray!50] (p-50) -- (p-51); \draw[line width=2,darkgray!50] (p-51) -- (p-26); \draw[line width=2,darkgray!50] (p-51) -- (p-24); \draw[line width=2,darkgray!50] (p-51) -- (p-52); \draw[line width=2,darkgray!50] (p-52) -- (p-28); \draw[line width=2,darkgray!50] (p-52) -- (p-53); \draw[line width=2,darkgray!50] (p-53) -- (p-34); \draw[line width=2,darkgray!50] (p-53) -- (p-54); \draw[line width=2,darkgray!50] (p-54) -- (p-38); \draw[line width=2,darkgray!50] (p-54) -- (p-36); \draw[line width=2,darkgray!50] (p-54) -- (p-55); \draw[line width=2,darkgray!50] (p-55) -- (p-42); \draw[line width=2,darkgray!50] (p-55) -- (p-40); \draw[line width=2,darkgray!50] (p-56) -- (p-46); \draw[line width=2,darkgray!50] (p-56) -- (p-4); \draw[line width=2,darkgray!50] (p-57) -- (p-56); \draw[line width=2,darkgray!50] (p-57) -- (p-5); \draw[line width=2,darkgray!50] (p-58) -- (p-57); \draw[line width=2,darkgray!50] (p-58) -- (p-5); \draw[line width=2,darkgray!50] (p-59) -- (p-58); \draw[line width=2,darkgray!50] (p-59) -- (p-60); \draw[line width=2,darkgray!50] (p-60) -- (p-44); \draw[line width=2,darkgray!50] (p-60) -- (p-56); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ \quoteon(2022-05-02 19:28 - haribo in Beitrag No. 2343) hab ein paar durchprobiert, das ist jetzt "PGF/TikZ" kannst du den jetzt öffnen? zeigt der bei dir dann auch auch beweglich 2-fach an wenn du den beweglich button drückst? \quoteoff Bei mir funktioniert bei dem Graph Button "tikz". Ist das die Eingabe, wo "tikz" nicht funktioniert hat? \quoteon(2022-05-06 10:57 - haribo in Beitrag No. 2364) jetzt gelingt es nichtmal mehr mit PGF/TikZ zu übertragen \quoteoff Kopiere die Eingabe in einen hide-Bereich wie zum Beispiel Slash in #2349 \quoteon(2022-05-07 07:08 - haribo in Beitrag No. 2365) Hab endlos viele EDIT Nachträge in meine letzten Beiträge nachgetragen... \quoteoff Hat genützt beim 4/8, danke 🙂 [Die Antwort wurde nach Beitrag No.2364 begonnen.]


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haribo
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  Beitrag No.2367, eingetragen 2022-05-07

Offenbar landen wir mit den Einsatzkantenbetrachtungen viel stärker in Richtung von statikfragen mit Bestimmtheit/Unbestimmtheit als bisher angenommen Beim 4/4 120er vermute ich das es mehr als vier EK gibt, aber hab auch noch keine auswahlkombinatiin erkannt welche die Beweglichkeit im gleichen grad belässt, dass müsste man aber ansich Stumpf durch Ausprobieren aller Kanten durchprobieren können, mal sehn ob das mit nem anderen statikprogram gelingt


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StefanVogel
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  Beitrag No.2368, eingetragen 2022-05-07

Das sehe ich auch so.


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haribo
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  Beitrag No.2369, eingetragen 2022-05-07

Deine Reduktion der EK‘s bei doppelkite‘s bedeutet wohl auch dass man alles nochmal überdenken muss... recht spannend diese Entwicklung Im besten Fall findet man dann weitere Einsparmöglichkeiten... könnte beim 4/11er was bringen


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haribo
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  Beitrag No.2370, eingetragen 2022-05-07

Man müsste den 120er irgendwie mit zusatzkonstruktionen (am besten aussenliegend damit sie nie stören) um seine vorhandene Beweglichkeit berauben/fixieren Dann würde evtl die EK Betrachtung einfacher weil dann wieder EK wäre was nicht beweglich macht... Hast du dazu ne Idee?


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StefanVogel
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  Beitrag No.2371, eingetragen 2022-05-07

Die Zusatzkonstruktion finden scheint gar nicht so einfach zu sein. Es müssen Kanten mit Länge 1 sein, sonst funktioniert Button "acos(1/4)" nicht richtig. Ich tippe darauf, daß das die Einsetzkanten nicht im geringsten stört und wieder die gleichen 4 Bereiche herauskommen.


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haribo
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  Beitrag No.2372, eingetragen 2022-05-07

Was bedeuten denn die Bereiche? Aus jedem eine EK?


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haribo
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  Beitrag No.2373, eingetragen 2022-05-07

bin immer noch am schnellsten wenn ich neuzeichne... er musste ja nicht in der symetrielage sein... idee war einen kite dranzulegen, oben ist dann die verbesserung davon https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-120fixiert.jpg


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StefanVogel
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  Beitrag No.2374, eingetragen 2022-05-07

Ja der geht. Je Bereich eine EK ist richtig. Warum das bei der Streichholzgraphensuche so sein muß, dafür überlege ich mir anhand dieses Graphen nochmal eine ausführliche Begründung. Bitte etwas Geduld... (Du kannst inzwischen noch ranbauen was du willst, die Bereiche der Einsetzkanten bleiben unverändert, wirst du sehen)


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haribo
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  Beitrag No.2375, eingetragen 2022-05-07

spinn off https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-4-4-228.JPG [Die Antwort wurde nach Beitrag No.2373 begonnen.]


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haribo
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  Beitrag No.2376, eingetragen 2022-05-07

also glaubst du der 120er hat einfach 4EK? passt dass zu den auf den 120er basierenden 4/5 [erfordert 4EK]; 4/6 [4EK]; 4/7[6EK]; 4/8 [6EK] ? [#2350; #2351, #2352] haben die also ihre teilweise, also jedenfals der 4/7 und 4/8er, zusätzlich erforderlichen zwei EK´s dann alle im mittelraum ? ich frag weil kites im mittelraum gibt es ja keine, dann muss es dort andere EK-generierende konstrukte geben, und die wären ja mal interessant herauszuarbeiten, insbesondere weil die ja evtl kleiner als kites sind? Nachtrag: könnte auch sein dass die innenkonstrukte im zusammenhang mit den äusseren wirken beim generieren von EK´s, dann sind sie möglöicherweise grösser als kites???


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haribo
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  Beitrag No.2377, eingetragen 2022-05-07

button acos1/4 ist bisher noch nicht in meinem verstehen angekommen


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haribo
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  Beitrag No.2378, eingetragen 2022-05-07

das der kite bei einzellast auf 12 NULLSTÄBE enthält hatten wir schonmal bemerkt den doppelkite hatten wir damals wohl nicht untersucht https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_statik-kite.jpg


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haribo
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  Beitrag No.2379, eingetragen 2022-05-07

Slash, der 4/10er und der 4/7 brauchen beide gleichviel EK‘s [6], weil der 10er knoten ja nur einmal da sein muss, da besteht an sich ne Chance dass man den 4/10er auch in den Rahmen des anderen unterbringt, fals Du mal puzzeln magst , weil sich selber unterbieten wäre ja nur der halbe spass


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Slash
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  Beitrag No.2380, vom Themenstarter, eingetragen 2022-05-07

\quoteon(2022-05-07 19:45 - haribo in Beitrag No. 2379) Slash, der 4/10er und der 4/7 brauchen beide gleichviel EK‘s [6], weil der 10er knoten ja nur einmal da sein muss, da besteht an sich ne Chance dass man den 4/10er auch in den Rahmen des anderen unterbringt, fals Du mal puzzeln magst , weil sich selber unterbieten wäre ja nur der halbe spass \quoteoff Ich habe gerade nicht so viel Zeit und Muße für Mathesachen, aber ich verfolge unseren Thread natürlich trotzdem so gut es geht mit.


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StefanVogel
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  Beitrag No.2381, eingetragen 2022-05-08

Jede Einsetzkante erzeugt einen Bereich von Zug- und Druckspannungen, wenn die Einsetzkante geringfügig ihre Länge ändern will. Diese Bereiche zu kennen ist nützlich für Button "Feinjustieren". Das will ich am Graph #2373 erläutern. Ich habe den zwischenzeitlichen Kite rechts unten wieder drangepackt, geht für den Zweck noch besser. 73 Knoten, 1×Grad 2, 3×Grad 3, 62×Grad 4, 3×Grad 5, 4×Grad 6, 0 Überschneidungen, 149 Kanten, minimal 0.99999999999999755751, maximal 1.00000000000000177636, Einsetzkanten=Beweglichkeit+6, $ %Eingabe war: % %Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % %P[1]=[0,-100]; P[2]=[50,-100]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2); N(46,6,3); N(47,10,8); N(48,14,12); N(49,18,16); N(50,22,20); N(51,26,24); N(52,30,28); N(53,34,32); N(54,38,36); N(55,42,40); N(56,46,4); N(57,56,5); L(58,57,5); L(59,57,58); N(60,44,55); A(58,45,Bew(5)); A(45,59,Bew(6)); A(59,60,Bew(6)); A(46,47,Bew(6)); A(47,48,Bew(6)); A(48,49,Bew(6)); A(49,50,Bew(6)); A(50,51,Bew(6)); A(51,52,Bew(6)); A(52,53,Bew(6)); A(53,54,Bew(6)); A(54,55,Bew(6)); A(60,56,Bew(6)); W(); L(61,23,25); L(62,61,25); Q(63,62,29,ab(1,2),ab(62,23,61,25)); RA(64,62); L(66,43,45); L(67,41,43); N(68,67,66); L(69,39,41); RA(66,67); Q(70,69,68,ab(1,2),ab(67,45,43,66,68)); RA(71,69); % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.42705098312484190970/0.00000000000000000000, 2/3.42705098312484190970/0.00000000000000000000, 3/2.92705098312484190970/0.86602540378443859659, 4/3.92705098312484190970/0.86602540378443848557, 5/4.42705098312484235379/0.00000000000000000000, 6/2.67705098312484190970/0.96824583655185425535, 7/1.71352549156242095485/0.70062926922203672131, 8/1.96352549156242095485/1.66887510577389086563, 9/1.00000000000000000000/1.40125853844407344262, 10/1.50000000000000000000/2.26728394222851203921, 11/0.50000000000000000000/2.26728394222851203921, 12/0.99999999999999966693/3.13330934601295041375, 13/0.00000000000000000000/3.13330934601294996966, 14/0.96352549156242106587/3.40092591334276805881, 15/0.25000000000000000000/4.10155518256480444705, 16/1.21352549156242095485/4.36917174989462164802, 17/0.50000000000000033307/5.06980101911665848036, 18/1.50000000000000022204/5.06980101911665848036, 19/1.00000000000000022204/5.93582642290109685490, 20/2.00000000000000000000/5.93582642290109774308, 21/1.50000000000000000000/6.80185182668553611762, 22/2.21352549156242117689/6.10122255746349839711, 23/2.46352549156242073281/7.06946839401535243042, 24/3.17705098312484190970/6.36883912479331648626, 25/3.42705098312484146561/7.33708496134517051956, 26/3.92705098312484146561/6.47105955756073214502, 27/4.42705098312484146561/7.33708496134517051956, 28/4.92705098312484146561/6.47105955756073214502, 29/5.42705098312484057743/7.33708496134517051956, 30/5.17705098312484057743/6.36883912479331648626, 31/6.14057647468726131024/6.63645569212313368723, 32/5.89057647468726131024/5.66820985557128054211, 33/6.85410196624968204304/5.93582642290109774308, 34/6.35410196624968204304/5.06980101911665848036, 35/7.35410196624968204304/5.06980101911665848036, 36/6.85410196624968204304/4.20377561533222010581, 37/7.85410196624968204304/4.20377561533222099399, 38/6.89057647468726131024/3.93615904800240334893, 39/7.60410196624968204304/3.23552977878036651660, 40/6.64057647468726131024/2.96791321145054887154, 41/7.35410196624968204304/2.26728394222851248330, 42/6.35410196624968204304/2.26728394222851292739, 43/6.85410196624968204304/1.40125853844407410875, 44/5.85410196624968204304/1.40125853844407410875, 45/6.35410196624968204304/0.53523313465963551216, 46/3.17705098312484190970/1.83427124033629307398, 47/2.46352549156242117689/2.53490050955832924018, 48/1.96352549156242095485/3.40092591334276672654, 49/2.21352549156242117689/4.36917174989462075985, 50/2.71352549156242028872/5.23519715367906002257, 51/3.67705098312484190970/5.50281372100887811172, 52/4.67705098312484057743/5.50281372100887811172, 53/5.39057647468726042206/4.80218445178684216756, 54/5.89057647468726131024/3.93615904800240290484, 55/5.64057647468726131024/2.96791321145054931563, 56/4.17705098312484235379/1.83427124033629262989, 57/4.67705098312484235379/0.96824583655185425535, 58/5.39057647468726397477/0.26761656732981720097, 59/5.64057647468726397477/1.23586240388167145632, 60/5.14057647468726131024/2.10188780766611094108, 61/2.71352549156241984463/8.03771423056720735190, 62/3.67705098312484146561/8.30533079789702632922, 63/4.53381372890605227610/8.82104156707044495533, 64/4.55205098312484057743/7.82120787962109798030, 65/5.40881372890605227610/8.33691864879451749459, 66/7.35410196624968204304/0.53523313465963551216, 67/7.85410196624968204304/1.40125853844407410875, 68/8.35410196624968115486/0.53523313465963529012, 69/8.31762745781210277585/2.53490050955833012836, 70/9.19262745781210277585/2.05077759128240311171, 71/8.33586471203089196536/1.53506682210898226515, 72/9.21086471203089196536/1.05094390383305591463, 73/10.06762745781210277585/1.56665467300647653914} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/60.00/75.52/0.4/Blue, 13/0.00/15.52/0.4/Blue, 21/300.00/315.52/0.4/Blue, 29/240.00/255.52/0.4/Blue, 37/180.00/195.52/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 15/13, 15/14, 16/15, 16/14, 17/15, 17/16, 18/17, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 27/25, 27/26, 28/27, 28/26, 29/27, 29/28, 30/29, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/33, 35/33, 35/34, 36/35, 36/34, 37/35, 37/36, 38/37, 39/37, 39/38, 40/39, 40/38, 41/39, 41/40, 42/41, 43/41, 43/42, 44/43, 44/42, 45/43, 45/44, 45/59, 46/6, 46/3, 46/47, 47/10, 47/8, 47/48, 48/14, 48/12, 48/49, 49/18, 49/16, 49/50, 50/22, 50/20, 50/51, 51/26, 51/24, 51/52, 52/30, 52/28, 52/53, 53/34, 53/32, 53/54, 54/38, 54/36, 54/55, 55/42, 55/40, 56/46, 56/4, 57/56, 57/5, 58/57, 58/5, 58/45, 59/57, 59/58, 59/60, 60/44, 60/55, 60/56, 61/23, 61/25, 62/61, 62/25, 63/62, 63/65, 63/64, 64/29, 64/65, 64/62, 65/29, 66/43, 66/45, 66/67, 67/41, 67/43, 68/67, 68/66, 68/71, 69/39, 69/41, 70/69, 70/71, 71/69, 72/71, 72/68, 72/70, 73/72, 73/70} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,73} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/60.00/75.52/0.4/Blue, 13/0.00/15.52/0.4/Blue, 21/300.00/315.52/0.4/Blue, 29/240.00/255.52/0.4/Blue, 37/180.00/195.52/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/286, 2/330, 3/150, 4/30, 5/330, 6/46, 7/286, 8/46, 9/166, 10/30, 11/210, 12/30, 13/150, 14/286, 15/106, 16/46, 17/210, 18/330, 19/210, 20/30, 21/166, 22/286, 23/106, 24/346, 25/46, 26/210, 27/150, 28/330, 29/106, 30/226, 31/46, 32/226, 33/346, 34/150, 35/330, 36/210, 37/330, 38/106, 39/106, 40/166, 41/286, 42/150, 43/330, 44/150, 45/210, 46/130, 47/340, 48/310, 49/280, 50/250, 51/340, 52/190, 53/160, 54/250, 55/100, 56/40, 57/106, 58/226, 59/106, 60/70, 61/106, 62/46, 63/121, 64/301, 65/1, 66/330, 67/330, 68/330, 69/121, 70/61, 71/241, 72/1, 73/1} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Der Graph ist starr und hat laut Abzählreim 6 Einsetzkanten. Button "acos(1/4)" hat dafür die Kanten P58-P59, P68-P71, P5-P58, P66-P67, P59-P60, P56-P60 ausgewählt und die Bereiche dafür bestimmt. Bereich 1 (hellblau): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.42705098312484190970/0.00000000000000000000, 2/3.42705098312484190970/0.00000000000000000000, 3/2.92705098312484190970/0.86602540378443881863, 4/3.92705098312484190970/0.86602540378443881863, 5/4.42705098312484235379/0.00000000000000028422, 6/2.67705098312484102152/0.96824583655185458841, 7/1.71352549156241984463/0.70062926922203583313, 8/1.96352549156241851236/1.66887510577389042155, 9/0.99999999999999744649/1.40125853844407166626, 10/1.49999999999999888978/2.26728394222850937467, 11/0.49999999999999855671/2.26728394222851115103, 12/1.00000000000000000000/3.13330934601294863739, 13/0.00000000000000000000/3.13330934601295041375, 14/0.96352549156242073281/3.40092591334276939108, 15/0.24999999999999858447/4.10155518256480533523, 16/1.21352549156241917849/4.36917174989462431256, 17/0.49999999999999689138/5.06980101911666025671, 18/1.49999999999999711342/5.06980101911665759218, 19/0.99999999999999888978/5.93582642290109774308, 20/1.99999999999999888978/5.93582642290109596672, 21/1.50000000000000022204/6.80185182668553611762, 22/2.21352549156242162098/6.10122255746349839711, 23/2.46352549156242117689/7.06946839401535243042, 24/3.17705098312484279788/6.36883912479331648626, 25/3.42705098312484190970/7.33708496134517051956, 26/3.92705098312484190970/6.47105955756073214502, 27/4.42705098312484235379/7.33708496134517051956, 28/4.92705098312484235379/6.47105955756073214502, 29/5.42705098312484235379/7.33708496134517051956, 30/5.17705098312484413015/6.36883912479331559808, 31/6.14057647468726486295/6.63645569212313635177, 32/5.89057647468726752749/5.66820985557128054211, 33/6.85410196624968737211/5.93582642290110040761, 34/6.35410196624968559576/5.06980101911666203307, 35/7.35410196624968559576/5.06980101911666025671, 36/6.85410196624968293122/4.20377561533222188217, 37/7.85410196624968381940/4.20377561533222099399, 38/6.89057647468726219842/3.93615904800240512529, 39/7.60410196624968293122/3.23552977878036696069, 40/6.64057647468726131024/2.96791321145055109199, 41/7.35410196624968204304/2.26728394222851381556, 42/6.35410196624968204304/2.26728394222851203921, 43/6.85410196624968293122/1.40125853844407410875, 44/5.85410196624968293122/1.40125853844407233240, 45/6.35410196624968381940/0.53523313465963473501, 46/3.17705098312484146561/1.83427124033629307398, 47/2.46352549156241940054/2.53490050955832835200, 48/1.96352549156242073281/3.40092591334276805881, 49/2.21352549156241940054/4.36917174989462253620, 50/2.71352549156242117689/5.23519715367906002257, 51/3.67705098312484190970/5.50281372100887811172, 52/4.67705098312484235379/5.50281372100887899990, 53/5.39057647468726486295/4.80218445178684394392, 54/5.89057647468726219842/3.93615904800240334893, 55/5.64057647468726131024/2.96791321145055020381, 56/4.17705098312484146561/1.83427124033629351807, 57/4.67705098312484235379/0.96824583655185458841, 58/5.39057647468726219842/0.26761656732981747853, 59/5.64057647468726219842/1.23586240388167145632, 60/5.14057647468726219842/2.10188780766611049700, 61/2.71352549156242028872/8.03771423056720735190, 62/3.67705098312484190970/8.30533079789702632922, 63/4.53381372890605316428/8.82104156707044495533, 64/4.55205098312484235379/7.82120787962109709213, 65/5.40881372890605316428/8.33691864879451749459, 66/7.35410196624968381940/0.53523313465963606728, 67/7.85410196624968293122/1.40125853844407544102, 68/8.35410196624968470758/0.53523313465963728852, 69/8.31762745781210277585/2.53490050955832968427, 70/9.19262745781210632856/2.05077759128240577624, 71/8.33586471203089729443/1.53506682210898248719, 72/9.21086471203089374171/1.05094390383305813508, 73/10.06762745781210632856/1.56665467300647787141} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-2) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-2); \draw[line width=2,blue!50] (p-4) -- (p-3); \draw[line width=2,blue!50] (p-4) -- (p-2); \draw[line width=2,blue!50] (p-5) -- (p-4); \draw[line width=2,blue!50] (p-5) -- (p-2); \draw[line width=2,blue!50] (p-6) -- (p-1); \draw[line width=2,blue!50] (p-6) -- (p-46); \draw[line width=2,blue!50] (p-7) -- (p-6); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-6); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-8); \draw[line width=2,blue!50] (p-10) -- (p-9); \draw[line width=2,blue!50] (p-10) -- (p-47); \draw[line width=2,blue!50] (p-11) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-12) -- (p-11); \draw[line width=2,blue!50] (p-12) -- (p-10); \draw[line width=2,blue!50] (p-13) -- (p-11); \draw[line width=2,blue!50] (p-13) -- (p-12); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-14) -- (p-48); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-14); \draw[line width=2,blue!50] (p-16) -- (p-15); \draw[line width=2,blue!50] (p-16) -- (p-14); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-18) -- (p-17); \draw[line width=2,blue!50] (p-18) -- (p-49); \draw[line width=2,blue!50] (p-19) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-19); \draw[line width=2,blue!50] (p-20) -- (p-18); \draw[line width=2,blue!50] (p-21) -- (p-19); \draw[line width=2,blue!50] (p-21) -- (p-20); \draw[line width=2,blue!50] (p-22) -- (p-21); \draw[line width=2,blue!50] (p-22) -- (p-50); \draw[line width=2,blue!50] (p-23) -- (p-21); \draw[line width=2,blue!50] (p-23) -- (p-22); \draw[line width=2,blue!50] (p-24) -- (p-23); \draw[line width=2,blue!50] (p-24) -- (p-22); \draw[line width=2,blue!50] (p-25) -- (p-23); \draw[line width=2,blue!50] (p-25) -- (p-24); \draw[line width=2,blue!50] (p-26) -- (p-25); \draw[line width=2,blue!50] (p-26) -- (p-51); \draw[line width=2,blue!50] (p-27) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-26); \draw[line width=2,blue!50] (p-28) -- (p-27); \draw[line width=2,blue!50] (p-28) -- (p-26); \draw[line width=2,blue!50] (p-29) -- (p-27); \draw[line width=2,blue!50] (p-29) -- (p-28); \draw[line width=2,blue!50] (p-30) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-30); \draw[line width=2,blue!50] (p-32) -- (p-31); \draw[line width=2,blue!50] (p-32) -- (p-30); \draw[line width=2,blue!50] (p-32) -- (p-53); \draw[line width=2,blue!50] (p-33) -- (p-31); \draw[line width=2,blue!50] (p-33) -- (p-32); \draw[line width=2,blue!50] (p-34) -- (p-33); \draw[line width=2,blue!50] (p-34) -- (p-53); \draw[line width=2,blue!50] (p-35) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-34); \draw[line width=2,blue!50] (p-35) -- (p-37); \draw[line width=2,blue!50] (p-36) -- (p-34); \draw[line width=2,blue!50] (p-36) -- (p-54); \draw[line width=2,blue!50] (p-36) -- (p-35); \draw[line width=2,blue!50] (p-36) -- (p-37); \draw[line width=2,blue!50] (p-37) -- (p-39); \draw[line width=2,blue!50] (p-38) -- (p-40); \draw[line width=2,blue!50] (p-38) -- (p-39); \draw[line width=2,blue!50] (p-39) -- (p-40); \draw[line width=2,blue!50] (p-39) -- (p-41); \draw[line width=2,blue!50] (p-40) -- (p-55); \draw[line width=2,blue!50] (p-40) -- (p-41); \draw[line width=2,blue!50] (p-41) -- (p-43); \draw[line width=2,blue!50] (p-42) -- (p-43); \draw[line width=2,blue!50] (p-42) -- (p-41); \draw[line width=2,blue!50] (p-42) -- (p-44); \draw[line width=2,blue!50] (p-43) -- (p-44); \draw[line width=2,blue!50] (p-43) -- (p-45); \draw[line width=2,blue!50] (p-44) -- (p-45); \draw[line width=2,blue!50] (p-45) -- (p-59); \draw[line width=2,blue!50] (p-45) -- (p-58); \draw[line width=2,blue!50] (p-46) -- (p-3); \draw[line width=2,blue!50] (p-46) -- (p-56); \draw[line width=2,blue!50] (p-47) -- (p-8); \draw[line width=2,blue!50] (p-47) -- (p-46); \draw[line width=2,blue!50] (p-48) -- (p-12); \draw[line width=2,blue!50] (p-49) -- (p-16); \draw[line width=2,blue!50] (p-49) -- (p-48); \draw[line width=2,blue!50] (p-50) -- (p-20); \draw[line width=2,blue!50] (p-50) -- (p-49); \draw[line width=2,blue!50] (p-51) -- (p-24); \draw[line width=2,blue!50] (p-51) -- (p-50); \draw[line width=2,blue!50] (p-52) -- (p-28); \draw[line width=2,blue!50] (p-52) -- (p-51); \draw[line width=2,blue!50] (p-53) -- (p-52); \draw[line width=2,blue!50] (p-53) -- (p-54); \draw[line width=2,blue!50] (p-54) -- (p-55); \draw[line width=2,blue!50] (p-54) -- (p-38); \draw[line width=2,blue!50] (p-55) -- (p-42); \draw[line width=2,blue!50] (p-56) -- (p-4); \draw[line width=2,blue!50] (p-56) -- (p-57); \draw[line width=2,blue!50] (p-57) -- (p-5); \draw[line width=2,blue!50] (p-57) -- (p-58); \draw[line width=2,blue!50] (p-59) -- (p-57); \draw[line width=2,blue!50] (p-59) -- (p-58); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 2 (orange): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.42705098312484190970/0.00000000000000000000, 2/3.42705098312484190970/0.00000000000000000000, 3/2.92705098312484190970/0.86602540378443881863, 4/3.92705098312484190970/0.86602540378443881863, 5/4.42705098312484235379/0.00000000000000028422, 6/2.67705098312484102152/0.96824583655185458841, 7/1.71352549156241984463/0.70062926922203583313, 8/1.96352549156241851236/1.66887510577389042155, 9/0.99999999999999744649/1.40125853844407166626, 10/1.49999999999999888978/2.26728394222850937467, 11/0.49999999999999855671/2.26728394222851115103, 12/1.00000000000000000000/3.13330934601294863739, 13/0.00000000000000000000/3.13330934601295041375, 14/0.96352549156242073281/3.40092591334276939108, 15/0.24999999999999858447/4.10155518256480533523, 16/1.21352549156241917849/4.36917174989462431256, 17/0.49999999999999689138/5.06980101911666025671, 18/1.49999999999999711342/5.06980101911665759218, 19/0.99999999999999888978/5.93582642290109774308, 20/1.99999999999999888978/5.93582642290109596672, 21/1.50000000000000022204/6.80185182668553611762, 22/2.21352549156242162098/6.10122255746349839711, 23/2.46352549156242117689/7.06946839401535243042, 24/3.17705098312484279788/6.36883912479331648626, 25/3.42705098312484190970/7.33708496134517051956, 26/3.92705098312484190970/6.47105955756073214502, 27/4.42705098312484235379/7.33708496134517051956, 28/4.92705098312484235379/6.47105955756073214502, 29/5.42705098312484235379/7.33708496134517051956, 30/5.17705098312484413015/6.36883912479331559808, 31/6.14057647468726486295/6.63645569212313635177, 32/5.89057647468726752749/5.66820985557128054211, 33/6.85410196624968737211/5.93582642290110040761, 34/6.35410196624968559576/5.06980101911666203307, 35/7.35410196624968559576/5.06980101911666025671, 36/6.85410196624968293122/4.20377561533222188217, 37/7.85410196624968381940/4.20377561533222099399, 38/6.89057647468726219842/3.93615904800240512529, 39/7.60410196624968293122/3.23552977878036696069, 40/6.64057647468726131024/2.96791321145055109199, 41/7.35410196624968204304/2.26728394222851381556, 42/6.35410196624968204304/2.26728394222851203921, 43/6.85410196624968293122/1.40125853844407410875, 44/5.85410196624968293122/1.40125853844407233240, 45/6.35410196624968381940/0.53523313465963473501, 46/3.17705098312484146561/1.83427124033629307398, 47/2.46352549156241940054/2.53490050955832835200, 48/1.96352549156242073281/3.40092591334276805881, 49/2.21352549156241940054/4.36917174989462253620, 50/2.71352549156242117689/5.23519715367906002257, 51/3.67705098312484190970/5.50281372100887811172, 52/4.67705098312484235379/5.50281372100887899990, 53/5.39057647468726486295/4.80218445178684394392, 54/5.89057647468726219842/3.93615904800240334893, 55/5.64057647468726131024/2.96791321145055020381, 56/4.17705098312484146561/1.83427124033629351807, 57/4.67705098312484235379/0.96824583655185458841, 58/5.39057647468726219842/0.26761656732981747853, 59/5.64057647468726219842/1.23586240388167145632, 60/5.14057647468726219842/2.10188780766611049700, 61/2.71352549156242028872/8.03771423056720735190, 62/3.67705098312484190970/8.30533079789702632922, 63/4.53381372890605316428/8.82104156707044495533, 64/4.55205098312484235379/7.82120787962109709213, 65/5.40881372890605316428/8.33691864879451749459, 66/7.35410196624968381940/0.53523313465963606728, 67/7.85410196624968293122/1.40125853844407544102, 68/8.35410196624968470758/0.53523313465963728852, 69/8.31762745781210277585/2.53490050955832968427, 70/9.19262745781210632856/2.05077759128240577624, 71/8.33586471203089729443/1.53506682210898248719, 72/9.21086471203089374171/1.05094390383305813508, 73/10.06762745781210632856/1.56665467300647787141} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,orange!50] (p-24) -- (p-23); \draw[line width=2,orange!50] (p-25) -- (p-23); \draw[line width=2,orange!50] (p-25) -- (p-24); \draw[line width=2,orange!50] (p-26) -- (p-25); \draw[line width=2,orange!50] (p-26) -- (p-51); \draw[line width=2,orange!50] (p-27) -- (p-25); \draw[line width=2,orange!50] (p-27) -- (p-26); \draw[line width=2,orange!50] (p-28) -- (p-27); \draw[line width=2,orange!50] (p-28) -- (p-26); \draw[line width=2,orange!50] (p-29) -- (p-27); \draw[line width=2,orange!50] (p-29) -- (p-28); \draw[line width=2,orange!50] (p-30) -- (p-29); \draw[line width=2,orange!50] (p-30) -- (p-52); \draw[line width=2,orange!50] (p-31) -- (p-29); \draw[line width=2,orange!50] (p-32) -- (p-30); \draw[line width=2,orange!50] (p-32) -- (p-53); \draw[line width=2,orange!50] (p-33) -- (p-31); \draw[line width=2,orange!50] (p-33) -- (p-32); \draw[line width=2,orange!50] (p-34) -- (p-33); \draw[line width=2,orange!50] (p-34) -- (p-53); \draw[line width=2,orange!50] (p-35) -- (p-33); \draw[line width=2,orange!50] (p-35) -- (p-37); \draw[line width=2,orange!50] (p-36) -- (p-34); \draw[line width=2,orange!50] (p-36) -- (p-54); \draw[line width=2,orange!50] (p-36) -- (p-37); \draw[line width=2,orange!50] (p-37) -- (p-38); \draw[line width=2,orange!50] (p-37) -- (p-39); \draw[line width=2,orange!50] (p-38) -- (p-40); \draw[line width=2,orange!50] (p-39) -- (p-40); \draw[line width=2,orange!50] (p-40) -- (p-55); \draw[line width=2,orange!50] (p-40) -- (p-41); \draw[line width=2,orange!50] (p-41) -- (p-43); \draw[line width=2,orange!50] (p-41) -- (p-67); \draw[line width=2,orange!50] (p-42) -- (p-43); \draw[line width=2,orange!50] (p-42) -- (p-41); \draw[line width=2,orange!50] (p-42) -- (p-44); \draw[line width=2,orange!50] (p-43) -- (p-44); \draw[line width=2,orange!50] (p-43) -- (p-45); \draw[line width=2,orange!50] (p-44) -- (p-45); \draw[line width=2,orange!50] (p-51) -- (p-24); \draw[line width=2,orange!50] (p-52) -- (p-28); \draw[line width=2,orange!50] (p-52) -- (p-51); \draw[line width=2,orange!50] (p-53) -- (p-52); \draw[line width=2,orange!50] (p-53) -- (p-54); \draw[line width=2,orange!50] (p-54) -- (p-55); \draw[line width=2,orange!50] (p-54) -- (p-38); \draw[line width=2,orange!50] (p-55) -- (p-42); \draw[line width=2,orange!50] (p-61) -- (p-23); \draw[line width=2,orange!50] (p-61) -- (p-25); \draw[line width=2,orange!50] (p-62) -- (p-61); \draw[line width=2,orange!50] (p-62) -- (p-25); \draw[line width=2,orange!50] (p-64) -- (p-29); \draw[line width=2,orange!50] (p-64) -- (p-62); \draw[line width=2,orange!50] (p-66) -- (p-45); \draw[line width=2,orange!50] (p-68) -- (p-67); \draw[line width=2,orange!50] (p-68) -- (p-66); \draw[line width=2,orange!50] (p-69) -- (p-39); \draw[line width=2,orange!50] (p-69) -- (p-41); \draw[line width=2,orange!50] (p-71) -- (p-69); \draw[line width=2,orange!50] (p-71) -- (p-68); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \draw (p-13) -- (p-12); \end{tikzpicture} $ Bereich 3 (purple) $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.42705098312484190970/0.00000000000000000000, 2/3.42705098312484190970/0.00000000000000000000, 3/2.92705098312484190970/0.86602540378443881863, 4/3.92705098312484190970/0.86602540378443881863, 5/4.42705098312484235379/0.00000000000000028422, 6/2.67705098312484102152/0.96824583655185458841, 7/1.71352549156241984463/0.70062926922203583313, 8/1.96352549156241851236/1.66887510577389042155, 9/0.99999999999999744649/1.40125853844407166626, 10/1.49999999999999888978/2.26728394222850937467, 11/0.49999999999999855671/2.26728394222851115103, 12/1.00000000000000000000/3.13330934601294863739, 13/0.00000000000000000000/3.13330934601295041375, 14/0.96352549156242073281/3.40092591334276939108, 15/0.24999999999999858447/4.10155518256480533523, 16/1.21352549156241917849/4.36917174989462431256, 17/0.49999999999999689138/5.06980101911666025671, 18/1.49999999999999711342/5.06980101911665759218, 19/0.99999999999999888978/5.93582642290109774308, 20/1.99999999999999888978/5.93582642290109596672, 21/1.50000000000000022204/6.80185182668553611762, 22/2.21352549156242162098/6.10122255746349839711, 23/2.46352549156242117689/7.06946839401535243042, 24/3.17705098312484279788/6.36883912479331648626, 25/3.42705098312484190970/7.33708496134517051956, 26/3.92705098312484190970/6.47105955756073214502, 27/4.42705098312484235379/7.33708496134517051956, 28/4.92705098312484235379/6.47105955756073214502, 29/5.42705098312484235379/7.33708496134517051956, 30/5.17705098312484413015/6.36883912479331559808, 31/6.14057647468726486295/6.63645569212313635177, 32/5.89057647468726752749/5.66820985557128054211, 33/6.85410196624968737211/5.93582642290110040761, 34/6.35410196624968559576/5.06980101911666203307, 35/7.35410196624968559576/5.06980101911666025671, 36/6.85410196624968293122/4.20377561533222188217, 37/7.85410196624968381940/4.20377561533222099399, 38/6.89057647468726219842/3.93615904800240512529, 39/7.60410196624968293122/3.23552977878036696069, 40/6.64057647468726131024/2.96791321145055109199, 41/7.35410196624968204304/2.26728394222851381556, 42/6.35410196624968204304/2.26728394222851203921, 43/6.85410196624968293122/1.40125853844407410875, 44/5.85410196624968293122/1.40125853844407233240, 45/6.35410196624968381940/0.53523313465963473501, 46/3.17705098312484146561/1.83427124033629307398, 47/2.46352549156241940054/2.53490050955832835200, 48/1.96352549156242073281/3.40092591334276805881, 49/2.21352549156241940054/4.36917174989462253620, 50/2.71352549156242117689/5.23519715367906002257, 51/3.67705098312484190970/5.50281372100887811172, 52/4.67705098312484235379/5.50281372100887899990, 53/5.39057647468726486295/4.80218445178684394392, 54/5.89057647468726219842/3.93615904800240334893, 55/5.64057647468726131024/2.96791321145055020381, 56/4.17705098312484146561/1.83427124033629351807, 57/4.67705098312484235379/0.96824583655185458841, 58/5.39057647468726219842/0.26761656732981747853, 59/5.64057647468726219842/1.23586240388167145632, 60/5.14057647468726219842/2.10188780766611049700, 61/2.71352549156242028872/8.03771423056720735190, 62/3.67705098312484190970/8.30533079789702632922, 63/4.53381372890605316428/8.82104156707044495533, 64/4.55205098312484235379/7.82120787962109709213, 65/5.40881372890605316428/8.33691864879451749459, 66/7.35410196624968381940/0.53523313465963606728, 67/7.85410196624968293122/1.40125853844407544102, 68/8.35410196624968470758/0.53523313465963728852, 69/8.31762745781210277585/2.53490050955832968427, 70/9.19262745781210632856/2.05077759128240577624, 71/8.33586471203089729443/1.53506682210898248719, 72/9.21086471203089374171/1.05094390383305813508, 73/10.06762745781210632856/1.56665467300647787141} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,purple!50] (p-2) -- (p-1); \draw[line width=2,purple!50] (p-3) -- (p-1); \draw[line width=2,purple!50] (p-3) -- (p-2); \draw[line width=2,purple!50] (p-4) -- (p-3); \draw[line width=2,purple!50] (p-4) -- (p-2); \draw[line width=2,purple!50] (p-5) -- (p-4); \draw[line width=2,purple!50] (p-5) -- (p-2); \draw[line width=2,purple!50] (p-6) -- (p-1); \draw[line width=2,purple!50] (p-6) -- (p-46); \draw[line width=2,purple!50] (p-7) -- (p-1); \draw[line width=2,purple!50] (p-7) -- (p-6); \draw[line width=2,purple!50] (p-8) -- (p-7); \draw[line width=2,purple!50] (p-8) -- (p-6); \draw[line width=2,purple!50] (p-9) -- (p-7); \draw[line width=2,purple!50] (p-9) -- (p-8); \draw[line width=2,purple!50] (p-10) -- (p-9); \draw[line width=2,purple!50] (p-10) -- (p-47); \draw[line width=2,purple!50] (p-11) -- (p-9); \draw[line width=2,purple!50] (p-11) -- (p-10); \draw[line width=2,purple!50] (p-12) -- (p-11); \draw[line width=2,purple!50] (p-12) -- (p-10); \draw[line width=2,purple!50] (p-13) -- (p-11); \draw[line width=2,purple!50] (p-13) -- (p-12); \draw[line width=2,purple!50] (p-14) -- (p-13); \draw[line width=2,purple!50] (p-14) -- (p-48); \draw[line width=2,purple!50] (p-15) -- (p-13); \draw[line width=2,purple!50] (p-15) -- (p-14); \draw[line width=2,purple!50] (p-16) -- (p-15); \draw[line width=2,purple!50] (p-16) -- (p-14); \draw[line width=2,purple!50] (p-17) -- (p-15); \draw[line width=2,purple!50] (p-17) -- (p-16); \draw[line width=2,purple!50] (p-18) -- (p-17); \draw[line width=2,purple!50] (p-18) -- (p-49); \draw[line width=2,purple!50] (p-19) -- (p-17); \draw[line width=2,purple!50] (p-19) -- (p-18); \draw[line width=2,purple!50] (p-20) -- (p-19); \draw[line width=2,purple!50] (p-20) -- (p-18); \draw[line width=2,purple!50] (p-21) -- (p-19); \draw[line width=2,purple!50] (p-21) -- (p-20); \draw[line width=2,purple!50] (p-23) -- (p-21); \draw[line width=2,purple!50] (p-25) -- (p-23); \draw[line width=2,purple!50] (p-26) -- (p-25); \draw[line width=2,purple!50] (p-26) -- (p-51); \draw[line width=2,purple!50] (p-27) -- (p-25); \draw[line width=2,purple!50] (p-27) -- (p-26); \draw[line width=2,purple!50] (p-28) -- (p-27); \draw[line width=2,purple!50] (p-28) -- (p-26); \draw[line width=2,purple!50] (p-29) -- (p-27); \draw[line width=2,purple!50] (p-29) -- (p-28); \draw[line width=2,purple!50] (p-30) -- (p-29); \draw[line width=2,purple!50] (p-30) -- (p-52); \draw[line width=2,purple!50] (p-31) -- (p-29); \draw[line width=2,purple!50] (p-31) -- (p-30); \draw[line width=2,purple!50] (p-32) -- (p-31); \draw[line width=2,purple!50] (p-32) -- (p-30); \draw[line width=2,purple!50] (p-32) -- (p-53); \draw[line width=2,purple!50] (p-33) -- (p-31); \draw[line width=2,purple!50] (p-33) -- (p-32); \draw[line width=2,purple!50] (p-34) -- (p-33); \draw[line width=2,purple!50] (p-34) -- (p-53); \draw[line width=2,purple!50] (p-35) -- (p-33); \draw[line width=2,purple!50] (p-35) -- (p-34); \draw[line width=2,purple!50] (p-35) -- (p-37); \draw[line width=2,purple!50] (p-36) -- (p-34); \draw[line width=2,purple!50] (p-36) -- (p-54); \draw[line width=2,purple!50] (p-36) -- (p-35); \draw[line width=2,purple!50] (p-36) -- (p-37); \draw[line width=2,purple!50] (p-37) -- (p-38); \draw[line width=2,purple!50] (p-37) -- (p-39); \draw[line width=2,purple!50] (p-38) -- (p-40); \draw[line width=2,purple!50] (p-38) -- (p-39); \draw[line width=2,purple!50] (p-39) -- (p-40); \draw[line width=2,purple!50] (p-39) -- (p-41); \draw[line width=2,purple!50] (p-40) -- (p-55); \draw[line width=2,purple!50] (p-40) -- (p-41); \draw[line width=2,purple!50] (p-41) -- (p-43); \draw[line width=2,purple!50] (p-42) -- (p-43); \draw[line width=2,purple!50] (p-42) -- (p-41); \draw[line width=2,purple!50] (p-42) -- (p-44); \draw[line width=2,purple!50] (p-43) -- (p-44); \draw[line width=2,purple!50] (p-43) -- (p-45); \draw[line width=2,purple!50] (p-44) -- (p-45); \draw[line width=2,purple!50] (p-45) -- (p-58); \draw[line width=2,purple!50] (p-46) -- (p-3); \draw[line width=2,purple!50] (p-47) -- (p-8); \draw[line width=2,purple!50] (p-47) -- (p-46); \draw[line width=2,purple!50] (p-48) -- (p-12); \draw[line width=2,purple!50] (p-48) -- (p-47); \draw[line width=2,purple!50] (p-49) -- (p-16); \draw[line width=2,purple!50] (p-49) -- (p-48); \draw[line width=2,purple!50] (p-50) -- (p-20); \draw[line width=2,purple!50] (p-50) -- (p-49); \draw[line width=2,purple!50] (p-51) -- (p-50); \draw[line width=2,purple!50] (p-52) -- (p-28); \draw[line width=2,purple!50] (p-52) -- (p-51); \draw[line width=2,purple!50] (p-53) -- (p-52); \draw[line width=2,purple!50] (p-53) -- (p-54); \draw[line width=2,purple!50] (p-54) -- (p-55); \draw[line width=2,purple!50] (p-54) -- (p-38); \draw[line width=2,purple!50] (p-55) -- (p-42); \draw[line width=2,purple!50] (p-58) -- (p-5); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 4 (hellgrau): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.42705098312484190970/0.00000000000000000000, 2/3.42705098312484190970/0.00000000000000000000, 3/2.92705098312484190970/0.86602540378443881863, 4/3.92705098312484190970/0.86602540378443881863, 5/4.42705098312484235379/0.00000000000000028422, 6/2.67705098312484102152/0.96824583655185458841, 7/1.71352549156241984463/0.70062926922203583313, 8/1.96352549156241851236/1.66887510577389042155, 9/0.99999999999999744649/1.40125853844407166626, 10/1.49999999999999888978/2.26728394222850937467, 11/0.49999999999999855671/2.26728394222851115103, 12/1.00000000000000000000/3.13330934601294863739, 13/0.00000000000000000000/3.13330934601295041375, 14/0.96352549156242073281/3.40092591334276939108, 15/0.24999999999999858447/4.10155518256480533523, 16/1.21352549156241917849/4.36917174989462431256, 17/0.49999999999999689138/5.06980101911666025671, 18/1.49999999999999711342/5.06980101911665759218, 19/0.99999999999999888978/5.93582642290109774308, 20/1.99999999999999888978/5.93582642290109596672, 21/1.50000000000000022204/6.80185182668553611762, 22/2.21352549156242162098/6.10122255746349839711, 23/2.46352549156242117689/7.06946839401535243042, 24/3.17705098312484279788/6.36883912479331648626, 25/3.42705098312484190970/7.33708496134517051956, 26/3.92705098312484190970/6.47105955756073214502, 27/4.42705098312484235379/7.33708496134517051956, 28/4.92705098312484235379/6.47105955756073214502, 29/5.42705098312484235379/7.33708496134517051956, 30/5.17705098312484413015/6.36883912479331559808, 31/6.14057647468726486295/6.63645569212313635177, 32/5.89057647468726752749/5.66820985557128054211, 33/6.85410196624968737211/5.93582642290110040761, 34/6.35410196624968559576/5.06980101911666203307, 35/7.35410196624968559576/5.06980101911666025671, 36/6.85410196624968293122/4.20377561533222188217, 37/7.85410196624968381940/4.20377561533222099399, 38/6.89057647468726219842/3.93615904800240512529, 39/7.60410196624968293122/3.23552977878036696069, 40/6.64057647468726131024/2.96791321145055109199, 41/7.35410196624968204304/2.26728394222851381556, 42/6.35410196624968204304/2.26728394222851203921, 43/6.85410196624968293122/1.40125853844407410875, 44/5.85410196624968293122/1.40125853844407233240, 45/6.35410196624968381940/0.53523313465963473501, 46/3.17705098312484146561/1.83427124033629307398, 47/2.46352549156241940054/2.53490050955832835200, 48/1.96352549156242073281/3.40092591334276805881, 49/2.21352549156241940054/4.36917174989462253620, 50/2.71352549156242117689/5.23519715367906002257, 51/3.67705098312484190970/5.50281372100887811172, 52/4.67705098312484235379/5.50281372100887899990, 53/5.39057647468726486295/4.80218445178684394392, 54/5.89057647468726219842/3.93615904800240334893, 55/5.64057647468726131024/2.96791321145055020381, 56/4.17705098312484146561/1.83427124033629351807, 57/4.67705098312484235379/0.96824583655185458841, 58/5.39057647468726219842/0.26761656732981747853, 59/5.64057647468726219842/1.23586240388167145632, 60/5.14057647468726219842/2.10188780766611049700, 61/2.71352549156242028872/8.03771423056720735190, 62/3.67705098312484190970/8.30533079789702632922, 63/4.53381372890605316428/8.82104156707044495533, 64/4.55205098312484235379/7.82120787962109709213, 65/5.40881372890605316428/8.33691864879451749459, 66/7.35410196624968381940/0.53523313465963606728, 67/7.85410196624968293122/1.40125853844407544102, 68/8.35410196624968470758/0.53523313465963728852, 69/8.31762745781210277585/2.53490050955832968427, 70/9.19262745781210632856/2.05077759128240577624, 71/8.33586471203089729443/1.53506682210898248719, 72/9.21086471203089374171/1.05094390383305813508, 73/10.06762745781210632856/1.56665467300647787141} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,darkgray!50] (p-41) -- (p-43); \draw[line width=2,darkgray!50] (p-41) -- (p-67); \draw[line width=2,darkgray!50] (p-42) -- (p-43); \draw[line width=2,darkgray!50] (p-42) -- (p-41); \draw[line width=2,darkgray!50] (p-42) -- (p-44); \draw[line width=2,darkgray!50] (p-43) -- (p-44); \draw[line width=2,darkgray!50] (p-43) -- (p-45); \draw[line width=2,darkgray!50] (p-44) -- (p-45); \draw[line width=2,darkgray!50] (p-66) -- (p-43); \draw[line width=2,darkgray!50] (p-66) -- (p-45); \draw[line width=2,darkgray!50] (p-67) -- (p-43); \draw[line width=2,darkgray!50] (p-67) -- (p-66); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \draw (p-13) -- (p-12); \end{tikzpicture} $ Bereich 5 (pink): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.42705098312484190970/0.00000000000000000000, 2/3.42705098312484190970/0.00000000000000000000, 3/2.92705098312484190970/0.86602540378443881863, 4/3.92705098312484190970/0.86602540378443881863, 5/4.42705098312484235379/0.00000000000000028422, 6/2.67705098312484102152/0.96824583655185458841, 7/1.71352549156241984463/0.70062926922203583313, 8/1.96352549156241851236/1.66887510577389042155, 9/0.99999999999999744649/1.40125853844407166626, 10/1.49999999999999888978/2.26728394222850937467, 11/0.49999999999999855671/2.26728394222851115103, 12/1.00000000000000000000/3.13330934601294863739, 13/0.00000000000000000000/3.13330934601295041375, 14/0.96352549156242073281/3.40092591334276939108, 15/0.24999999999999858447/4.10155518256480533523, 16/1.21352549156241917849/4.36917174989462431256, 17/0.49999999999999689138/5.06980101911666025671, 18/1.49999999999999711342/5.06980101911665759218, 19/0.99999999999999888978/5.93582642290109774308, 20/1.99999999999999888978/5.93582642290109596672, 21/1.50000000000000022204/6.80185182668553611762, 22/2.21352549156242162098/6.10122255746349839711, 23/2.46352549156242117689/7.06946839401535243042, 24/3.17705098312484279788/6.36883912479331648626, 25/3.42705098312484190970/7.33708496134517051956, 26/3.92705098312484190970/6.47105955756073214502, 27/4.42705098312484235379/7.33708496134517051956, 28/4.92705098312484235379/6.47105955756073214502, 29/5.42705098312484235379/7.33708496134517051956, 30/5.17705098312484413015/6.36883912479331559808, 31/6.14057647468726486295/6.63645569212313635177, 32/5.89057647468726752749/5.66820985557128054211, 33/6.85410196624968737211/5.93582642290110040761, 34/6.35410196624968559576/5.06980101911666203307, 35/7.35410196624968559576/5.06980101911666025671, 36/6.85410196624968293122/4.20377561533222188217, 37/7.85410196624968381940/4.20377561533222099399, 38/6.89057647468726219842/3.93615904800240512529, 39/7.60410196624968293122/3.23552977878036696069, 40/6.64057647468726131024/2.96791321145055109199, 41/7.35410196624968204304/2.26728394222851381556, 42/6.35410196624968204304/2.26728394222851203921, 43/6.85410196624968293122/1.40125853844407410875, 44/5.85410196624968293122/1.40125853844407233240, 45/6.35410196624968381940/0.53523313465963473501, 46/3.17705098312484146561/1.83427124033629307398, 47/2.46352549156241940054/2.53490050955832835200, 48/1.96352549156242073281/3.40092591334276805881, 49/2.21352549156241940054/4.36917174989462253620, 50/2.71352549156242117689/5.23519715367906002257, 51/3.67705098312484190970/5.50281372100887811172, 52/4.67705098312484235379/5.50281372100887899990, 53/5.39057647468726486295/4.80218445178684394392, 54/5.89057647468726219842/3.93615904800240334893, 55/5.64057647468726131024/2.96791321145055020381, 56/4.17705098312484146561/1.83427124033629351807, 57/4.67705098312484235379/0.96824583655185458841, 58/5.39057647468726219842/0.26761656732981747853, 59/5.64057647468726219842/1.23586240388167145632, 60/5.14057647468726219842/2.10188780766611049700, 61/2.71352549156242028872/8.03771423056720735190, 62/3.67705098312484190970/8.30533079789702632922, 63/4.53381372890605316428/8.82104156707044495533, 64/4.55205098312484235379/7.82120787962109709213, 65/5.40881372890605316428/8.33691864879451749459, 66/7.35410196624968381940/0.53523313465963606728, 67/7.85410196624968293122/1.40125853844407544102, 68/8.35410196624968470758/0.53523313465963728852, 69/8.31762745781210277585/2.53490050955832968427, 70/9.19262745781210632856/2.05077759128240577624, 71/8.33586471203089729443/1.53506682210898248719, 72/9.21086471203089374171/1.05094390383305813508, 73/10.06762745781210632856/1.56665467300647787141} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,pink!50] (p-2) -- (p-1); \draw[line width=2,pink!50] (p-3) -- (p-1); \draw[line width=2,pink!50] (p-3) -- (p-2); \draw[line width=2,pink!50] (p-4) -- (p-3); \draw[line width=2,pink!50] (p-4) -- (p-2); \draw[line width=2,pink!50] (p-5) -- (p-4); \draw[line width=2,pink!50] (p-5) -- (p-2); \draw[line width=2,pink!50] (p-6) -- (p-1); \draw[line width=2,pink!50] (p-6) -- (p-46); \draw[line width=2,pink!50] (p-7) -- (p-6); \draw[line width=2,pink!50] (p-8) -- (p-7); \draw[line width=2,pink!50] (p-8) -- (p-6); \draw[line width=2,pink!50] (p-9) -- (p-7); \draw[line width=2,pink!50] (p-9) -- (p-8); \draw[line width=2,pink!50] (p-10) -- (p-9); \draw[line width=2,pink!50] (p-10) -- (p-47); \draw[line width=2,pink!50] (p-11) -- (p-9); \draw[line width=2,pink!50] (p-11) -- (p-10); \draw[line width=2,pink!50] (p-12) -- (p-11); \draw[line width=2,pink!50] (p-12) -- (p-10); \draw[line width=2,pink!50] (p-13) -- (p-11); \draw[line width=2,pink!50] (p-13) -- (p-12); \draw[line width=2,pink!50] (p-14) -- (p-13); \draw[line width=2,pink!50] (p-14) -- (p-48); \draw[line width=2,pink!50] (p-15) -- (p-13); \draw[line width=2,pink!50] (p-15) -- (p-14); \draw[line width=2,pink!50] (p-16) -- (p-15); \draw[line width=2,pink!50] (p-16) -- (p-14); \draw[line width=2,pink!50] (p-17) -- (p-15); \draw[line width=2,pink!50] (p-17) -- (p-16); \draw[line width=2,pink!50] (p-18) -- (p-17); \draw[line width=2,pink!50] (p-18) -- (p-49); \draw[line width=2,pink!50] (p-19) -- (p-17); \draw[line width=2,pink!50] (p-19) -- (p-18); \draw[line width=2,pink!50] (p-20) -- (p-19); \draw[line width=2,pink!50] (p-20) -- (p-18); \draw[line width=2,pink!50] (p-21) -- (p-19); \draw[line width=2,pink!50] (p-21) -- (p-20); \draw[line width=2,pink!50] (p-22) -- (p-21); \draw[line width=2,pink!50] (p-22) -- (p-50); \draw[line width=2,pink!50] (p-23) -- (p-21); \draw[line width=2,pink!50] (p-24) -- (p-22); \draw[line width=2,pink!50] (p-25) -- (p-23); \draw[line width=2,pink!50] (p-25) -- (p-24); \draw[line width=2,pink!50] (p-26) -- (p-25); \draw[line width=2,pink!50] (p-26) -- (p-51); \draw[line width=2,pink!50] (p-27) -- (p-25); \draw[line width=2,pink!50] (p-27) -- (p-26); \draw[line width=2,pink!50] (p-28) -- (p-27); \draw[line width=2,pink!50] (p-28) -- (p-26); \draw[line width=2,pink!50] (p-29) -- (p-27); \draw[line width=2,pink!50] (p-29) -- (p-28); \draw[line width=2,pink!50] (p-30) -- (p-29); \draw[line width=2,pink!50] (p-30) -- (p-52); \draw[line width=2,pink!50] (p-31) -- (p-29); \draw[line width=2,pink!50] (p-31) -- (p-30); \draw[line width=2,pink!50] (p-32) -- (p-31); \draw[line width=2,pink!50] (p-32) -- (p-30); \draw[line width=2,pink!50] (p-32) -- (p-53); \draw[line width=2,pink!50] (p-33) -- (p-31); \draw[line width=2,pink!50] (p-33) -- (p-32); \draw[line width=2,pink!50] (p-34) -- (p-33); \draw[line width=2,pink!50] (p-34) -- (p-53); \draw[line width=2,pink!50] (p-35) -- (p-33); \draw[line width=2,pink!50] (p-35) -- (p-34); \draw[line width=2,pink!50] (p-35) -- (p-37); \draw[line width=2,pink!50] (p-36) -- (p-34); \draw[line width=2,pink!50] (p-36) -- (p-54); \draw[line width=2,pink!50] (p-36) -- (p-35); \draw[line width=2,pink!50] (p-36) -- (p-37); \draw[line width=2,pink!50] (p-37) -- (p-38); \draw[line width=2,pink!50] (p-37) -- (p-39); \draw[line width=2,pink!50] (p-38) -- (p-40); \draw[line width=2,pink!50] (p-38) -- (p-39); \draw[line width=2,pink!50] (p-39) -- (p-40); \draw[line width=2,pink!50] (p-40) -- (p-55); \draw[line width=2,pink!50] (p-40) -- (p-41); \draw[line width=2,pink!50] (p-41) -- (p-43); \draw[line width=2,pink!50] (p-42) -- (p-43); \draw[line width=2,pink!50] (p-42) -- (p-41); \draw[line width=2,pink!50] (p-42) -- (p-44); \draw[line width=2,pink!50] (p-43) -- (p-44); \draw[line width=2,pink!50] (p-43) -- (p-45); \draw[line width=2,pink!50] (p-44) -- (p-60); \draw[line width=2,pink!50] (p-44) -- (p-45); \draw[line width=2,pink!50] (p-45) -- (p-59); \draw[line width=2,pink!50] (p-46) -- (p-3); \draw[line width=2,pink!50] (p-46) -- (p-56); \draw[line width=2,pink!50] (p-47) -- (p-8); \draw[line width=2,pink!50] (p-47) -- (p-46); \draw[line width=2,pink!50] (p-48) -- (p-12); \draw[line width=2,pink!50] (p-48) -- (p-47); \draw[line width=2,pink!50] (p-49) -- (p-16); \draw[line width=2,pink!50] (p-49) -- (p-48); \draw[line width=2,pink!50] (p-50) -- (p-20); \draw[line width=2,pink!50] (p-50) -- (p-49); \draw[line width=2,pink!50] (p-51) -- (p-24); \draw[line width=2,pink!50] (p-51) -- (p-50); \draw[line width=2,pink!50] (p-52) -- (p-28); \draw[line width=2,pink!50] (p-52) -- (p-51); \draw[line width=2,pink!50] (p-53) -- (p-52); \draw[line width=2,pink!50] (p-53) -- (p-54); \draw[line width=2,pink!50] (p-54) -- (p-55); \draw[line width=2,pink!50] (p-54) -- (p-38); \draw[line width=2,pink!50] (p-55) -- (p-60); \draw[line width=2,pink!50] (p-55) -- (p-42); \draw[line width=2,pink!50] (p-56) -- (p-4); \draw[line width=2,pink!50] (p-56) -- (p-57); \draw[line width=2,pink!50] (p-57) -- (p-5); \draw[line width=2,pink!50] (p-59) -- (p-57); \draw[line width=2,pink!50] (p-60) -- (p-59); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 6 (grün): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.42705098312484190970/0.00000000000000000000, 2/3.42705098312484190970/0.00000000000000000000, 3/2.92705098312484190970/0.86602540378443881863, 4/3.92705098312484190970/0.86602540378443881863, 5/4.42705098312484235379/0.00000000000000028422, 6/2.67705098312484102152/0.96824583655185458841, 7/1.71352549156241984463/0.70062926922203583313, 8/1.96352549156241851236/1.66887510577389042155, 9/0.99999999999999744649/1.40125853844407166626, 10/1.49999999999999888978/2.26728394222850937467, 11/0.49999999999999855671/2.26728394222851115103, 12/1.00000000000000000000/3.13330934601294863739, 13/0.00000000000000000000/3.13330934601295041375, 14/0.96352549156242073281/3.40092591334276939108, 15/0.24999999999999858447/4.10155518256480533523, 16/1.21352549156241917849/4.36917174989462431256, 17/0.49999999999999689138/5.06980101911666025671, 18/1.49999999999999711342/5.06980101911665759218, 19/0.99999999999999888978/5.93582642290109774308, 20/1.99999999999999888978/5.93582642290109596672, 21/1.50000000000000022204/6.80185182668553611762, 22/2.21352549156242162098/6.10122255746349839711, 23/2.46352549156242117689/7.06946839401535243042, 24/3.17705098312484279788/6.36883912479331648626, 25/3.42705098312484190970/7.33708496134517051956, 26/3.92705098312484190970/6.47105955756073214502, 27/4.42705098312484235379/7.33708496134517051956, 28/4.92705098312484235379/6.47105955756073214502, 29/5.42705098312484235379/7.33708496134517051956, 30/5.17705098312484413015/6.36883912479331559808, 31/6.14057647468726486295/6.63645569212313635177, 32/5.89057647468726752749/5.66820985557128054211, 33/6.85410196624968737211/5.93582642290110040761, 34/6.35410196624968559576/5.06980101911666203307, 35/7.35410196624968559576/5.06980101911666025671, 36/6.85410196624968293122/4.20377561533222188217, 37/7.85410196624968381940/4.20377561533222099399, 38/6.89057647468726219842/3.93615904800240512529, 39/7.60410196624968293122/3.23552977878036696069, 40/6.64057647468726131024/2.96791321145055109199, 41/7.35410196624968204304/2.26728394222851381556, 42/6.35410196624968204304/2.26728394222851203921, 43/6.85410196624968293122/1.40125853844407410875, 44/5.85410196624968293122/1.40125853844407233240, 45/6.35410196624968381940/0.53523313465963473501, 46/3.17705098312484146561/1.83427124033629307398, 47/2.46352549156241940054/2.53490050955832835200, 48/1.96352549156242073281/3.40092591334276805881, 49/2.21352549156241940054/4.36917174989462253620, 50/2.71352549156242117689/5.23519715367906002257, 51/3.67705098312484190970/5.50281372100887811172, 52/4.67705098312484235379/5.50281372100887899990, 53/5.39057647468726486295/4.80218445178684394392, 54/5.89057647468726219842/3.93615904800240334893, 55/5.64057647468726131024/2.96791321145055020381, 56/4.17705098312484146561/1.83427124033629351807, 57/4.67705098312484235379/0.96824583655185458841, 58/5.39057647468726219842/0.26761656732981747853, 59/5.64057647468726219842/1.23586240388167145632, 60/5.14057647468726219842/2.10188780766611049700, 61/2.71352549156242028872/8.03771423056720735190, 62/3.67705098312484190970/8.30533079789702632922, 63/4.53381372890605316428/8.82104156707044495533, 64/4.55205098312484235379/7.82120787962109709213, 65/5.40881372890605316428/8.33691864879451749459, 66/7.35410196624968381940/0.53523313465963606728, 67/7.85410196624968293122/1.40125853844407544102, 68/8.35410196624968470758/0.53523313465963728852, 69/8.31762745781210277585/2.53490050955832968427, 70/9.19262745781210632856/2.05077759128240577624, 71/8.33586471203089729443/1.53506682210898248719, 72/9.21086471203089374171/1.05094390383305813508, 73/10.06762745781210632856/1.56665467300647787141} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,green!50] (p-2) -- (p-1); \draw[line width=2,green!50] (p-3) -- (p-1); \draw[line width=2,green!50] (p-3) -- (p-2); \draw[line width=2,green!50] (p-4) -- (p-3); \draw[line width=2,green!50] (p-4) -- (p-2); \draw[line width=2,green!50] (p-6) -- (p-1); \draw[line width=2,green!50] (p-6) -- (p-46); \draw[line width=2,green!50] (p-7) -- (p-6); \draw[line width=2,green!50] (p-8) -- (p-7); \draw[line width=2,green!50] (p-8) -- (p-6); \draw[line width=2,green!50] (p-9) -- (p-7); \draw[line width=2,green!50] (p-9) -- (p-8); \draw[line width=2,green!50] (p-10) -- (p-9); \draw[line width=2,green!50] (p-10) -- (p-47); \draw[line width=2,green!50] (p-11) -- (p-9); \draw[line width=2,green!50] (p-11) -- (p-10); \draw[line width=2,green!50] (p-12) -- (p-11); \draw[line width=2,green!50] (p-12) -- (p-10); \draw[line width=2,green!50] (p-13) -- (p-11); \draw[line width=2,green!50] (p-13) -- (p-12); \draw[line width=2,green!50] (p-14) -- (p-13); \draw[line width=2,green!50] (p-14) -- (p-48); \draw[line width=2,green!50] (p-15) -- (p-13); \draw[line width=2,green!50] (p-15) -- (p-14); \draw[line width=2,green!50] (p-16) -- (p-15); \draw[line width=2,green!50] (p-16) -- (p-14); \draw[line width=2,green!50] (p-17) -- (p-15); \draw[line width=2,green!50] (p-17) -- (p-16); \draw[line width=2,green!50] (p-18) -- (p-17); \draw[line width=2,green!50] (p-18) -- (p-49); \draw[line width=2,green!50] (p-19) -- (p-17); \draw[line width=2,green!50] (p-19) -- (p-18); \draw[line width=2,green!50] (p-20) -- (p-19); \draw[line width=2,green!50] (p-20) -- (p-18); \draw[line width=2,green!50] (p-21) -- (p-19); \draw[line width=2,green!50] (p-21) -- (p-20); \draw[line width=2,green!50] (p-23) -- (p-21); \draw[line width=2,green!50] (p-25) -- (p-23); \draw[line width=2,green!50] (p-26) -- (p-25); \draw[line width=2,green!50] (p-26) -- (p-51); \draw[line width=2,green!50] (p-27) -- (p-25); \draw[line width=2,green!50] (p-27) -- (p-26); \draw[line width=2,green!50] (p-28) -- (p-27); \draw[line width=2,green!50] (p-28) -- (p-26); \draw[line width=2,green!50] (p-29) -- (p-27); \draw[line width=2,green!50] (p-29) -- (p-28); \draw[line width=2,green!50] (p-30) -- (p-29); \draw[line width=2,green!50] (p-30) -- (p-52); \draw[line width=2,green!50] (p-31) -- (p-29); \draw[line width=2,green!50] (p-31) -- (p-30); \draw[line width=2,green!50] (p-32) -- (p-31); \draw[line width=2,green!50] (p-32) -- (p-30); \draw[line width=2,green!50] (p-32) -- (p-53); \draw[line width=2,green!50] (p-33) -- (p-31); \draw[line width=2,green!50] (p-33) -- (p-32); \draw[line width=2,green!50] (p-34) -- (p-33); \draw[line width=2,green!50] (p-34) -- (p-53); \draw[line width=2,green!50] (p-35) -- (p-33); \draw[line width=2,green!50] (p-35) -- (p-34); \draw[line width=2,green!50] (p-35) -- (p-37); \draw[line width=2,green!50] (p-36) -- (p-34); \draw[line width=2,green!50] (p-36) -- (p-54); \draw[line width=2,green!50] (p-36) -- (p-35); \draw[line width=2,green!50] (p-36) -- (p-37); \draw[line width=2,green!50] (p-37) -- (p-38); \draw[line width=2,green!50] (p-37) -- (p-39); \draw[line width=2,green!50] (p-38) -- (p-40); \draw[line width=2,green!50] (p-38) -- (p-39); \draw[line width=2,green!50] (p-39) -- (p-40); \draw[line width=2,green!50] (p-40) -- (p-55); \draw[line width=2,green!50] (p-40) -- (p-41); \draw[line width=2,green!50] (p-41) -- (p-43); \draw[line width=2,green!50] (p-42) -- (p-43); \draw[line width=2,green!50] (p-42) -- (p-41); \draw[line width=2,green!50] (p-42) -- (p-44); \draw[line width=2,green!50] (p-43) -- (p-44); \draw[line width=2,green!50] (p-44) -- (p-60); \draw[line width=2,green!50] (p-46) -- (p-3); \draw[line width=2,green!50] (p-46) -- (p-56); \draw[line width=2,green!50] (p-47) -- (p-8); \draw[line width=2,green!50] (p-47) -- (p-46); \draw[line width=2,green!50] (p-48) -- (p-12); \draw[line width=2,green!50] (p-48) -- (p-47); \draw[line width=2,green!50] (p-49) -- (p-16); \draw[line width=2,green!50] (p-49) -- (p-48); \draw[line width=2,green!50] (p-50) -- (p-20); \draw[line width=2,green!50] (p-50) -- (p-49); \draw[line width=2,green!50] (p-51) -- (p-50); \draw[line width=2,green!50] (p-52) -- (p-28); \draw[line width=2,green!50] (p-52) -- (p-51); \draw[line width=2,green!50] (p-53) -- (p-52); \draw[line width=2,green!50] (p-53) -- (p-54); \draw[line width=2,green!50] (p-54) -- (p-55); \draw[line width=2,green!50] (p-54) -- (p-38); \draw[line width=2,green!50] (p-55) -- (p-60); \draw[line width=2,green!50] (p-55) -- (p-42); \draw[line width=2,green!50] (p-56) -- (p-4); \draw[line width=2,green!50] (p-60) -- (p-56); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Jetzt lege ich die Betrachtung mit den Einsetzkanten und deren Bereichen erstmal zur Seite. Ich gebe den Graph neu ein allein mit den Eingabefunktionen N(zwei Kanten als Dreieck anfügen) und M(eine Kante in einem Winkel anfügen). Das sind Eingabefunktionen, die nur mit Kantenlänge 1 ausgeführt werden und deshalb passen. Ich zeichne nur einen Graph, die einzelnen Teilschritte kann man mit Button "Beschreibung" sichtbar machen und dort jeden einzelnen Eingabeschritt anklicken. Bei den Punkten P5, P29, P68 geht es mit Eingabefunktion N nicht weiter, deshalb dort die Fortsetzung mit Eingabefunktion M. 73 Knoten, 6×Grad 2, 11×Grad 3, 49×Grad 4, 3×Grad 5, 4×Grad 6, 0 Überschneidungen, 140 Kanten, minimal 0.99999999999999944489, maximal 1.00000000000000111022, Einsetzkanten=Beweglichkeit-3, $ %Eingabe war: % %Automatisch generierte Eingabe zu: Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % % % %P[1]=[0,-100]; P[2]=[50,-100]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(58,5,4,blauerWinkel); N(57,5,58); N(59,57,58); N(45,59,58); N(56,4,57); N(60,56,59); N(44,60,45); N(46,3,56); N(6,1,46); N(7,1,6); N(8,7,6); N(9,7,8); N(43,44,45); N(47,8,46); N(66,43,45); N(67,43,66); N(68,67,66); N(10,9,47); N(11,9,10); N(12,11,10); N(13,11,12); N(41,43,67); N(42,43,41); N(48,12,47); N(55,60,42); N(14,13,48); N(15,13,14); N(16,15,14); N(17,15,16); N(40,55,41); N(49,16,48); N(18,17,49); N(19,17,18); N(20,19,18); N(21,19,20); N(39,40,41); N(50,20,49); N(69,39,41); N(22,21,50); N(23,21,22); N(24,23,22); N(25,23,24); N(38,40,39); N(51,24,50); N(54,55,38); N(61,23,25); N(62,61,25); N(26,25,51); N(27,25,26); N(28,27,26); N(29,27,28); N(37,38,39); N(52,28,51); N(53,52,54); N(30,29,52); N(31,29,30); N(32,31,30); N(33,31,32); N(34,33,53); N(35,33,34); N(36,35,34); M(72,68,67,gruenerWinkel); N(70,69,72); N(71,68,70); N(73,70,72); M(65,29,27,orangerWinkel); N(63,62,65); N(64,29,63); % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.53/0.00, 2/3.53/0.00, 3/3.03/0.87, 4/4.03/0.87, 5/4.53/0.00, 6/2.71/0.98, 7/1.77/0.64, 8/1.94/1.63, 9/1.00/1.29, 10/1.50/2.15, 11/0.50/2.15, 12/1.00/3.02, 13/0.00/3.02, 14/0.94/3.36, 15/0.17/4.00, 16/1.11/4.34, 17/0.35/4.99, 18/1.35/4.99, 19/0.85/5.85, 20/1.85/5.85, 21/1.35/6.72, 22/2.11/6.08, 23/2.29/7.06, 24/3.05/6.42, 25/3.23/7.40, 26/3.73/6.54, 27/4.23/7.40, 28/4.73/6.54, 29/5.23/7.40, 30/5.05/6.42, 31/5.99/6.76, 32/5.82/5.78, 33/6.76/6.12, 34/6.26/5.25, 35/7.26/5.25, 36/6.76/4.39, 37/7.76/4.39, 38/6.82/4.04, 39/7.59/3.40, 40/6.65/3.06, 41/7.41/2.42, 42/6.41/2.42, 43/6.91/1.55, 44/5.91/1.55, 45/6.41/0.68, 46/3.21/1.85, 47/2.44/2.49, 48/1.94/3.36, 49/2.11/4.34, 50/2.61/5.21, 51/3.55/5.55, 52/4.55/5.55, 53/5.32/4.91, 54/5.82/4.04, 55/5.65/3.06, 56/4.21/1.85, 57/4.71/0.98, 58/5.47/0.34, 59/5.65/1.33, 60/5.15/2.19, 61/2.46/8.05, 62/3.40/8.39, 63/4.31/8.80, 64/4.31/7.80, 65/5.23/8.40, 66/7.41/0.68, 67/7.91/1.55, 68/8.41/0.68, 69/8.35/2.76, 70/9.25/2.32, 71/8.49/1.68, 72/9.18/1.33, 73/10.08/1.76} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/120.00/380.00/0.4/Blue, 68/120.00/400.00/0.4/Green, 29/180.00/450.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/46, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 10/47, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 14/48, 15/13, 15/14, 16/15, 16/14, 17/15, 17/16, 18/17, 18/49, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 22/50, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 26/51, 27/25, 27/26, 28/27, 28/26, 29/27, 29/28, 30/29, 30/52, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/33, 34/53, 35/33, 35/34, 36/35, 36/34, 37/38, 37/39, 38/40, 38/39, 39/40, 39/41, 40/55, 40/41, 41/43, 41/67, 42/43, 42/41, 43/44, 43/45, 44/60, 44/45, 45/59, 45/58, 46/3, 46/56, 47/8, 47/46, 48/12, 48/47, 49/16, 49/48, 50/20, 50/49, 51/24, 51/50, 52/28, 52/51, 53/52, 53/54, 54/55, 54/38, 55/60, 55/42, 56/4, 56/57, 57/5, 57/58, 58/5, 59/57, 59/58, 60/56, 60/59, 61/23, 61/25, 62/61, 62/25, 63/62, 63/65, 64/29, 64/63, 65/29, 66/43, 66/45, 67/43, 67/66, 68/67, 68/66, 69/39, 69/41, 70/69, 70/72, 71/68, 71/70, 72/68, 73/70, 73/72} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,73} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/120.00/380.00/0.4/Blue, 68/120.00/400.00/0.4/Green, 29/180.00/450.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/290, 2/330, 3/90, 4/30, 5/330, 6/50, 7/170, 8/50, 9/170, 10/330, 11/150, 12/30, 13/230, 14/290, 15/230, 16/50, 17/210, 18/330, 19/150, 20/330, 21/170, 22/230, 23/170, 24/350, 25/350, 26/210, 27/30, 28/330, 29/110, 30/230, 31/50, 32/230, 33/90, 34/210, 35/30, 36/270, 37/50, 38/170, 39/350, 40/170, 41/90, 42/150, 43/90, 44/150, 45/210, 46/13, 47/103, 48/73, 49/43, 50/13, 51/223, 52/313, 53/163, 54/133, 55/223, 56/43, 57/110, 58/230, 59/50, 60/192, 61/170, 62/50, 63/60, 64/216, 65/36, 66/210, 67/30, 68/330, 69/350, 70/116, 71/155, 72/236, 73/356} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Alle Knoten sind plaziert. Ich ergänze noch die 9 fehlenden Kanten mit Eingabefunktion A(eine Kante zwischen zwei vorhandene Knoten einfügen). Ob die Kanten passen, das kommt darauf an, ob die Knoten schon im richtigen Abstand liegen. Button "alle A(j,k)" über dem Graph zeigt die aktuellen Kantenlängen. 73 Knoten, 1×Grad 2, 3×Grad 3, 62×Grad 4, 3×Grad 5, 4×Grad 6, 0 Überschneidungen, 149 Kanten, minimal 0.77705453925868384069, maximal 1.09555042728824592047, Einsetzkanten=Beweglichkeit+6, einzustellende Kanten, Abstände und Winkel: nicht passende Kanten: |P64-P65|=1.09555042728824592047 |P64-P62|=1.08159430691728042362 |P71-P72|=0.77705453925868384069 |P71-P69|=1.08526112490131354527 $ %Eingabe war: % %Automatisch generierte Eingabe zu: Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % % % %P[1]=[0,-100]; P[2]=[50,-100]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(58,5,4,blauerWinkel); N(57,5,58); N(59,57,58); N(45,59,58); N(56,4,57); N(60,56,59); N(44,60,45); N(46,3,56); N(6,1,46); N(7,1,6); N(8,7,6); N(9,7,8); N(43,44,45); N(47,8,46); N(66,43,45); N(67,43,66); N(68,67,66); N(10,9,47); N(11,9,10); N(12,11,10); N(13,11,12); N(41,43,67); N(42,43,41); N(48,12,47); N(55,60,42); N(14,13,48); N(15,13,14); N(16,15,14); N(17,15,16); N(40,55,41); N(49,16,48); N(18,17,49); N(19,17,18); N(20,19,18); N(21,19,20); N(39,40,41); N(50,20,49); N(69,39,41); N(22,21,50); N(23,21,22); N(24,23,22); N(25,23,24); N(38,40,39); N(51,24,50); N(54,55,38); N(61,23,25); N(62,61,25); N(26,25,51); N(27,25,26); N(28,27,26); N(29,27,28); N(37,38,39); N(52,28,51); N(53,52,54); N(30,29,52); N(31,29,30); N(32,31,30); N(33,31,32); N(34,33,53); N(35,33,34); N(36,35,34); M(72,68,67,gruenerWinkel); N(70,69,72); N(71,68,70); N(73,70,72); M(65,29,27,orangerWinkel); N(63,62,65); N(64,29,63); %A(42,44); %A(32,53); %A(35,37); %A(36,37); %A(36,54); %A(71,72); %A(64,65); %A(64,62); %A(71,69); % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.53208888623795624895/0.00000000000000000000, 2/3.53208888623795624895/0.00000000000000000000, 3/3.03208888623795624895/0.86602540378443881863, 4/4.03208888623795669304/0.86602540378443881863, 5/4.53208888623795669304/0.00000000000000028422, 6/2.70573706390488588625/0.98480775301220813134, 7/1.76604444311897790243/0.64278760968653902985, 8/1.93969262078590820586/1.62759536269874693915, 9/0.99999999999999966693/1.28557521937307805970, 10/1.49999999999999977796/2.15160062315751643425, 11/0.49999999999999972244/2.15160062315751687834, 12/0.99999999999999966693/3.01762602694195569697, 13/0.00000000000000000000/3.01762602694195480879, 14/0.93969262078590820586/3.35964617026762413232, 15/0.17364817766692966505/4.00243377995416338422, 16/1.11334079845283784316/4.34445392327983270775, 17/0.34729635533385933011/4.98724153296637151556, 18/1.34729635533385927459/4.98724153296637151556, 19/0.84729635533385927459/5.85326693675081077828, 20/1.84729635533385927459/5.85326693675081077828, 21/1.34729635533385994073/6.71929234053524826464, 22/2.11334079845283806520/6.07650473084871034501, 23/2.28698897611976814659/7.06131248386091758817, 24/3.05303341923874649311/6.41852487417437966855, 25/3.22668159690567568632/7.40333262718658691171, 26/3.72668159690567657449/6.53730722340214942534, 27/4.22668159690567524223/7.40333262718658868806, 28/4.72668159690567701858/6.53730722340215031352, 29/5.22668159690567524223/7.40333262718658957624, 30/5.05303341923874516084/6.41852487417438144490, 31/5.99272604002465403283/6.76054501750005076843, 32/5.81907786235772395145/5.77573726448784174892, 33/6.75877048314363193526/6.11775740781351018427, 34/6.25877048314362127712/5.25173200402907802697, 35/7.25877048314362127712/5.25173200402906648065, 36/6.75877048314361239534/4.38570660024463343518, 37/7.75877048314363459980/4.38570660024463077065, 38/6.81907786235772661598/4.04368645691896144712, 39/7.58512230547670451841/3.40089884723242219522, 40/6.64542968469079742277/3.05887870390675331578, 41/7.41147412780977532520/2.41609109422021406388, 42/6.41147412780977710156/2.41609109422021628433, 43/6.91147412780977443703/1.55006569043577657752, 44/5.91147412780977443703/1.55006569043577857592, 45/6.41147412780977177249/0.68404028665133898013, 46/3.20573706390488588625/1.85083315679664672793, 47/2.43969262078590798382/2.49362076648318620187, 48/1.93969262078590820586/3.35964617026762502050, 49/2.11334079845283806520/4.34445392327983270775, 50/2.61334079845283850929/5.21047932706427197047, 51/3.55303341923874649311/5.55249947038994129400, 52/4.55303341923874693720/5.55249947038994129400, 53/5.31907786235771862238/4.90971186070339538077, 54/5.81907786235772661598/4.04368645691896144712, 55/5.64542968469079742277/3.05887870390675420396, 56/4.20573706390488588625/1.85083315679664672793, 57/4.70573706390488588625/0.98480775301220835338, 58/5.47178150702386467685/0.34202014332566932353, 59/5.64542968469079387006/1.32682789633787767691, 60/5.14542968469079475824/2.19285330012231627350, 61/2.46063715378669733980/8.04612023687312571951, 62/3.40032977457260532361/8.38814038019879504304, 63/4.31011611523920201705/8.80321725782085984235, 64/4.31011611523920290523/7.80321725782085895418, 65/5.22668159690567435405/8.40333262718658957624, 66/7.41147412780977177249/0.68404028665133698173, 67/7.91147412780977443703/1.55006569043577435707, 68/8.41147412780977177249/0.68404028665133442821, 69/8.35116674859568242084/2.75811123754588383150, 70/9.25204851301303676792/2.32404667260159270015, 71/8.48600406989405620095/1.68125906291505544665, 72/9.17751857092875056310/1.32682789633787145966, 73/10.07840033534610668653/1.76089246128215792808} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/120.00/380.00/0.4/Blue, 68/120.00/400.00/0.4/Green, 29/180.00/450.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[very thick,green] (p-42) -- (p-44); \draw[very thick,green] (p-32) -- (p-53); \draw[very thick,green] (p-35) -- (p-37); \draw[very thick,green] (p-36) -- (p-37); \draw[very thick,green] (p-36) -- (p-54); \draw[very thick,green] (p-71) -- (p-72); \draw[very thick,green] (p-64) -- (p-65); \draw[very thick,green] (p-64) -- (p-62); \draw[very thick,green] (p-71) -- (p-69); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/46, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 10/47, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 14/48, 15/13, 15/14, 16/15, 16/14, 17/15, 17/16, 18/17, 18/49, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 22/50, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 26/51, 27/25, 27/26, 28/27, 28/26, 29/27, 29/28, 30/29, 30/52, 31/29, 31/30, 32/31, 32/30, 32/53, 33/31, 33/32, 34/33, 34/53, 35/33, 35/34, 35/37, 36/35, 36/34, 36/37, 36/54, 37/38, 37/39, 38/40, 38/39, 39/40, 39/41, 40/55, 40/41, 41/43, 41/67, 42/43, 42/41, 42/44, 43/44, 43/45, 44/60, 44/45, 45/59, 45/58, 46/3, 46/56, 47/8, 47/46, 48/12, 48/47, 49/16, 49/48, 50/20, 50/49, 51/24, 51/50, 52/28, 52/51, 53/52, 53/54, 54/55, 54/38, 55/60, 55/42, 56/4, 56/57, 57/5, 57/58, 58/5, 59/57, 59/58, 60/56, 60/59, 61/23, 61/25, 62/61, 62/25, 63/62, 63/65, 64/29, 64/63, 64/65, 64/62, 65/29, 66/43, 66/45, 67/43, 67/66, 68/67, 68/66, 69/39, 69/41, 70/69, 70/72, 71/68, 71/70, 71/72, 71/69, 72/68, 73/70, 73/72} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-65); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-62); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-71) -- (p-72); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-71) -- (p-69); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/120.00/380.00/0.4/Blue, 68/120.00/400.00/0.4/Green, 29/180.00/450.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/290, 2/330, 3/90, 4/30, 5/330, 6/50, 7/170, 8/50, 9/170, 10/330, 11/150, 12/30, 13/230, 14/290, 15/230, 16/50, 17/210, 18/330, 19/150, 20/330, 21/170, 22/230, 23/170, 24/350, 25/350, 26/210, 27/30, 28/330, 29/110, 30/230, 31/50, 32/230, 33/90, 34/210, 35/30, 36/210, 37/330, 38/170, 39/350, 40/170, 41/90, 42/90, 43/90, 44/210, 45/210, 46/13, 47/103, 48/73, 49/43, 50/13, 51/223, 52/313, 53/282, 54/253, 55/223, 56/43, 57/110, 58/230, 59/50, 60/192, 61/170, 62/50, 63/57, 64/64, 65/216, 66/210, 67/30, 68/330, 69/350, 70/116, 71/119, 72/236, 73/356} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Fünf von den 9 Kanten haben bis auf angesammelte Rundungsfehler schon die passende Länge. Sie behalten auch die passende Länge, wenn man die drei Winkel etwas variiert, sind deshalb soweit fertig. Aber diese Kanten noch nicht aus dem Blickfeld verlieren, sie werden nochmal gebraucht! Die vier verbleibenden Kanten müssen jetzt noch zurechtgezogen werden mit den drei beweglichen Winkeln. Bei nur einem Winkel kann man diesen hin und her variieren, bis man eine Kante passend hinbekommen hat. Auch bei zwei Winkeln ist es noch zu schaffen, mit hin und her variieren zwei Kanten passend zu machen. Für drei Winkel war ursprünglich ein Button "Feinjustieren(3,3)" vorgesehen, er befindet sich inzwischen unter Button "ausführlich" wenn man diesen anklickt. Dazu musste man drei Kanten kennzeichnen mittels zusätzlicher Eingabe "R(i,j)" oder Umschreiben von "A(i,j)" in "RA(i,j)", wenn man Kante Pi-Pj einstellen will. Nachdem man drei solche Kanten bestimmt hat, kann man mit Button "neu zeichnen" und Button "Feinjustieren(3,3)" die Kanten zurechtziehen und manchmal hat das Zurechtziehen funktioniert, manchmal auch nicht. Im vorliegenden Graph stehen vier nicht passende Kanten A(71,72); A(64,65); A(64,62); A(71,69) zur Auswahl. Davon drei auswählen und Button "Feinjustieren(3,3)" ergibt folgende Ergebnisse RA(71,72); RA(64,65); RA(64,62); A(71,69); Graph wird passend zurechtgezogen, RA(71,72); RA(64,65); A(64,62); RA(71,69); Graph wird passend zurechtgezogen, RA(71,72); A(64,65); RA(64,62); RA(71,69); keine stabile Lösung, A(71,72); RA(64,65); RA(64,62); RA(71,69); keine stabile Lösung. Bei drei beweglichen Winkeln und vier einzustellenden Kanten diese verschiedenen Varianten durchprobieren war schon machbar. Bei zwölf Winkeln und 15 einzustellenden Kanten geht das nicht mehr. Wie muss ich die Kanten auswählen, damit Button Feinjustieren funktioniert? Jetzt kommen die Bereiche der Einsetzkanten zum Zuge. Von den neun Kanten wähle ich 3 Kanten so aus, dass jede der übrigen Kanten genau einem Bereich zugeordnet werden kann, in dem sie auch enthalten ist, und jeder Bereich genau einmal verwendet wird. Beim aktuellen Graph sind die 9 zuletzt eingefügten Kanten in folgenden Bereichen enthalten: P32-P53 liegt in Bereich 0 1 2 4 5 P64-P62 liegt in Bereich 1 P36-P37 liegt in Bereich 0 1 2 4 5 P36-P35 liegt in Bereich 0 2 4 5 P35-P37 liegt in Bereich 0 1 2 4 5 P42-P44 liegt in Bereich 0 1 2 3 4 5 P64-P65 liegt in Bereich P71-P72 liegt in Bereich P71-P69 liegt in Bereich 1 Es geht nur RA(71,72); RA(64,65); RA(64,62); und RA(71,72); RA(64,65); RA(71,60), weil P64-P65 und P71-P72 gar keinem Bereich zugeordnet werden können. Eine mögliche Zuordnung ist dann P32-P53 zu Bereich 0 P36-P37 zu Bereich 2 P36-P35 zu Bereich 4 P35-P37 zu Bereich 5 P42-P44 zu Bereich 3 und P64-P62 oder P71-P69 zu Bereich 1 je nachdem welche nicht in RA(...) verwendet wurde Button "Feinjustieren" macht diese Auswahl schon seit einiger Zeit automatisch und ergänzt dann die Auswahl im großen Eingabefenster.


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haribo
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  Beitrag No.2382, eingetragen 2022-05-08

Orange is toll, würde der Bereich sich komplett herumziehen wenn der kite links oben an-läge also von P17 bis P 23 ?


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StefanVogel
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  Beitrag No.2383, eingetragen 2022-05-08

Von P17 bis P23, dann passt der Kite aber nicht in P21 ran. Dort ist ein anderer Winkel als in P41 und P25. Soll ich deshalb P13 bis P19 mit Winkel in P17 nehmen?


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haribo
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  Beitrag No.2384, eingetragen 2022-05-08

Ich brauch auch bald ne Pause, für neue Horizonte , aber jetzt noch nicht, Am 4/10er überlegt, wir wissen er braucht 6 EK‘s , 3 für den 4/4er Anteil plus 6 halbe für die anderen 6 Hölzer im 10er Knoten Es muss also letztlich irgendwie eine Verbindung von jeder EK zu jedem der 10 Hölzer im 10er geben weil ja jedes der 10 Hölzer irgendwann eingepasst werden könnte , Also ist jedes der 10 eine EK? Wir wissen beim 4/10er dass wir weitere EK‘s immer mit kites generiert haben, und kennen im kite jetzt genau welche Hölzer EK s generieren, die letzten zwei erforderlichen EK generieren wir mit der unteren Krebsschere, also ziemlich weit entfernt vom 10er Knoten Mit deinen Bereichen muss also wohl von der Krebsschere auch eine durchgehende bereichsverbindung bestehen bis zum 10er? Durchgehend weil sonst ja keine kraftübertragung durchgeleitet werden könnte Und weil wir in rekordgraphen keine überflüssigen Hölzer einbauen, muss auch gelten: jedes Holz muss mindestens in einem Bereich eingebunden sein? Oder sogar in mehreren? Verwirrend, bis gestern dachte ich man kann einzelne EK s suchen und finden, jetzt scheint zu gelten dass man nur die Bereiche finden kann und jedes darin enthaltene Holz könnte jeweils einzeln für sich genommen das notwendige EK sein? Die doppelkites sind dann damit also EK Generatoren über oft weit verlaufende Bereiche? Dito beim 4/11er Monster von jeder Krebsschere bis zu den Kernen gibt es jeweils durchgehende Verbinder-Bereiche ??? [Die Antwort wurde nach Beitrag No.2382 begonnen.]


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haribo
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  Beitrag No.2385, eingetragen 2022-05-08

\quoteon(2022-05-08 06:55 - StefanVogel in Beitrag No. 2383) Von P17 bis P23, dann passt der Kite aber nicht in P21 ran. Dort ist ein anderer Winkel als in P41 und P25. Soll ich deshalb P13 bis P19 mit Winkel in P17 nehmen? \quoteoff Stimmt, dann leg ihn doch testweise von P15 bis P 21 Egal 13 bis 19 ist auch gut Die Frage ist ob die Verbindung dann nicht einen kürzeren Weg wählt als um den ganzen Graphen herum , und fals die das macht , wann schwipp t das um


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
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  Beitrag No.2386, eingetragen 2022-05-08

P15 bis P21 habe ich genommen. Das ist 180° rotationssysmmetrisch. 76 Knoten, 2×Grad 2, 66×Grad 4, 4×Grad 5, 4×Grad 6, 0 Überschneidungen, 156 Kanten, minimal 0.99999999999999678035, maximal 1.00000000000000444089, Einsetzkanten=Beweglichkeit+7, einzustellende Kanten, Abstände und Winkel: $ %Eingabe war: % %Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % %P[1]=[88.77040952594916,-44.677831990038186]; P[2]=[135.0511491964971,-25.754483038360235]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2); N(46,6,3); N(47,10,8); N(48,14,12); N(49,18,16); N(50,22,20); N(51,26,24); N(52,30,28); N(53,34,32); N(54,38,36); N(55,42,40); N(56,46,4); N(57,56,5); L(58,57,5); L(59,57,58); N(60,44,55); A(58,45,Bew(5)); A(45,59,Bew(6)); A(59,60,Bew(6)); A(46,47,Bew(6)); A(47,48,Bew(6)); A(48,49,Bew(6)); A(49,50,Bew(6)); A(50,51,Bew(6)); A(51,52,Bew(6)); A(52,53,Bew(6)); A(53,54,Bew(6)); A(54,55,Bew(6)); A(60,56,Bew(6)); L(61,15,17); L(62,17,19); L(63,19,21); A(62,63); L(64,62,63); %Q(65,61,64,ab(1,2),ab(62,21,19,63,64)); A(61,66); L(69,39,41); L(70,41,43); L(71,43,45); A(70,71); L(72,70,71); Q(73,69,72,ab(1,2),ab(70,45,43,71,72)); A(74,69); % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/5.57, 64/1.20/5.19, 65/0.99/3.47, 66/1.59/4.27, 67/0.60/4.39, 68/0.00/3.58, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/82.24/97.76/0.4/Blue, 13/22.24/37.76/0.4/Blue, 21/322.24/337.76/0.4/Blue, 29/262.24/277.76/0.4/Blue, 37/202.24/217.76/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 15/13, 15/14, 16/15, 16/14, 17/15, 17/16, 18/17, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 27/25, 27/26, 28/27, 28/26, 29/27, 29/28, 30/29, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/33, 35/33, 35/34, 36/35, 36/34, 37/35, 37/36, 38/37, 39/37, 39/38, 40/39, 40/38, 41/39, 41/40, 42/41, 43/41, 43/42, 44/43, 44/42, 45/43, 45/44, 45/59, 46/6, 46/3, 46/47, 47/10, 47/8, 47/48, 48/14, 48/12, 48/49, 49/18, 49/16, 49/50, 50/22, 50/20, 50/51, 51/26, 51/24, 51/52, 52/30, 52/28, 52/53, 53/34, 53/32, 53/54, 54/38, 54/36, 54/55, 55/42, 55/40, 56/46, 56/4, 57/56, 57/5, 58/57, 58/5, 58/45, 59/57, 59/58, 59/60, 60/44, 60/55, 60/56, 61/15, 61/17, 61/66, 62/17, 62/19, 62/63, 63/19, 63/21, 64/62, 64/63, 64/66, 65/61, 65/66, 65/67, 67/66, 67/64, 68/65, 68/67, 69/39, 69/41, 70/41, 70/43, 70/71, 71/43, 71/45, 72/70, 72/71, 72/74, 73/69, 73/74, 73/75, 74/69, 75/74, 75/72, 76/73, 76/75} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,76} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/82.24/97.76/0.4/Blue, 13/22.24/37.76/0.4/Blue, 21/322.24/337.76/0.4/Blue, 29/262.24/277.76/0.4/Blue, 37/202.24/217.76/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/308, 2/352, 3/172, 4/52, 5/352, 6/8, 7/188, 8/128, 9/188, 10/352, 11/172, 12/52, 13/172, 14/8, 15/128, 16/8, 17/68, 18/352, 19/292, 20/352, 21/52, 22/248, 23/128, 24/8, 25/68, 26/232, 27/52, 28/292, 29/52, 30/248, 31/8, 32/248, 33/8, 34/232, 35/52, 36/232, 37/352, 38/188, 39/8, 40/188, 41/52, 42/172, 43/52, 44/232, 45/8, 46/32, 47/2, 48/332, 49/302, 50/272, 51/242, 52/333, 53/182, 54/152, 55/243, 56/182, 57/128, 58/308, 59/68, 60/213, 61/323, 62/232, 63/52, 64/172, 65/263, 66/323, 67/203, 68/203, 69/143, 70/112, 71/292, 72/263, 73/23, 74/143, 75/323, 76/23} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Button "acos(1/4)" hat folgende 7 Einsetzkanten P55-P60 P45-P71 P69-P74 P56-P60 P45-P58 P21-P63 P58-P59 gewählt und dazu folgende Bereiche bestimmt. Bereich 1 (hellblau): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/5.57, 64/1.20/5.19, 65/0.99/3.47, 66/1.59/4.27, 67/0.60/4.39, 68/0.00/3.58, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-65); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-2) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-2); \draw[line width=2,blue!50] (p-4) -- (p-3); \draw[line width=2,blue!50] (p-4) -- (p-2); \draw[line width=2,blue!50] (p-5) -- (p-4); \draw[line width=2,blue!50] (p-5) -- (p-2); \draw[line width=2,blue!50] (p-6) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-6); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-6); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-8); \draw[line width=2,blue!50] (p-10) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-12) -- (p-11); \draw[line width=2,blue!50] (p-12) -- (p-10); \draw[line width=2,blue!50] (p-13) -- (p-11); \draw[line width=2,blue!50] (p-13) -- (p-12); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-14); \draw[line width=2,blue!50] (p-16) -- (p-15); \draw[line width=2,blue!50] (p-16) -- (p-14); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-18) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-19); \draw[line width=2,blue!50] (p-20) -- (p-18); \draw[line width=2,blue!50] (p-21) -- (p-19); \draw[line width=2,blue!50] (p-21) -- (p-20); \draw[line width=2,blue!50] (p-22) -- (p-21); \draw[line width=2,blue!50] (p-23) -- (p-21); \draw[line width=2,blue!50] (p-24) -- (p-22); \draw[line width=2,blue!50] (p-25) -- (p-23); \draw[line width=2,blue!50] (p-25) -- (p-24); \draw[line width=2,blue!50] (p-26) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-26); \draw[line width=2,blue!50] (p-28) -- (p-27); \draw[line width=2,blue!50] (p-28) -- (p-26); \draw[line width=2,blue!50] (p-29) -- (p-27); \draw[line width=2,blue!50] (p-29) -- (p-28); \draw[line width=2,blue!50] (p-30) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-30); \draw[line width=2,blue!50] (p-32) -- (p-31); \draw[line width=2,blue!50] (p-32) -- (p-30); \draw[line width=2,blue!50] (p-33) -- (p-31); \draw[line width=2,blue!50] (p-33) -- (p-32); \draw[line width=2,blue!50] (p-34) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-34); \draw[line width=2,blue!50] (p-36) -- (p-35); \draw[line width=2,blue!50] (p-36) -- (p-34); \draw[line width=2,blue!50] (p-37) -- (p-35); \draw[line width=2,blue!50] (p-37) -- (p-36); \draw[line width=2,blue!50] (p-38) -- (p-37); \draw[line width=2,blue!50] (p-39) -- (p-37); \draw[line width=2,blue!50] (p-39) -- (p-38); \draw[line width=2,blue!50] (p-40) -- (p-39); \draw[line width=2,blue!50] (p-40) -- (p-38); \draw[line width=2,blue!50] (p-41) -- (p-40); \draw[line width=2,blue!50] (p-42) -- (p-41); \draw[line width=2,blue!50] (p-43) -- (p-41); \draw[line width=2,blue!50] (p-43) -- (p-42); \draw[line width=2,blue!50] (p-44) -- (p-43); \draw[line width=2,blue!50] (p-44) -- (p-42); \draw[line width=2,blue!50] (p-45) -- (p-43); \draw[line width=2,blue!50] (p-45) -- (p-44); \draw[line width=2,blue!50] (p-45) -- (p-59); \draw[line width=2,blue!50] (p-46) -- (p-6); \draw[line width=2,blue!50] (p-46) -- (p-3); \draw[line width=2,blue!50] (p-46) -- (p-47); \draw[line width=2,blue!50] (p-47) -- (p-10); \draw[line width=2,blue!50] (p-47) -- (p-8); \draw[line width=2,blue!50] (p-47) -- (p-48); \draw[line width=2,blue!50] (p-48) -- (p-14); \draw[line width=2,blue!50] (p-48) -- (p-12); \draw[line width=2,blue!50] (p-48) -- (p-49); \draw[line width=2,blue!50] (p-49) -- (p-18); \draw[line width=2,blue!50] (p-49) -- (p-16); \draw[line width=2,blue!50] (p-49) -- (p-50); \draw[line width=2,blue!50] (p-50) -- (p-22); \draw[line width=2,blue!50] (p-50) -- (p-20); \draw[line width=2,blue!50] (p-50) -- (p-51); \draw[line width=2,blue!50] (p-51) -- (p-26); \draw[line width=2,blue!50] (p-51) -- (p-24); \draw[line width=2,blue!50] (p-51) -- (p-52); \draw[line width=2,blue!50] (p-52) -- (p-30); \draw[line width=2,blue!50] (p-52) -- (p-28); \draw[line width=2,blue!50] (p-52) -- (p-53); \draw[line width=2,blue!50] (p-53) -- (p-34); \draw[line width=2,blue!50] (p-53) -- (p-32); \draw[line width=2,blue!50] (p-53) -- (p-54); \draw[line width=2,blue!50] (p-54) -- (p-38); \draw[line width=2,blue!50] (p-54) -- (p-36); \draw[line width=2,blue!50] (p-54) -- (p-55); \draw[line width=2,blue!50] (p-55) -- (p-42); \draw[line width=2,blue!50] (p-55) -- (p-40); \draw[line width=2,blue!50] (p-56) -- (p-46); \draw[line width=2,blue!50] (p-56) -- (p-4); \draw[line width=2,blue!50] (p-57) -- (p-56); \draw[line width=2,blue!50] (p-57) -- (p-5); \draw[line width=2,blue!50] (p-59) -- (p-57); \draw[line width=2,blue!50] (p-59) -- (p-60); \draw[line width=2,blue!50] (p-60) -- (p-44); \draw[line width=2,blue!50] (p-60) -- (p-55); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 2 (orange): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/5.57, 64/1.20/5.19, 65/0.99/3.47, 66/1.59/4.27, 67/0.60/4.39, 68/0.00/3.58, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-65); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,orange!50] (p-42) -- (p-41); \draw[line width=2,orange!50] (p-43) -- (p-41); \draw[line width=2,orange!50] (p-43) -- (p-42); \draw[line width=2,orange!50] (p-44) -- (p-43); \draw[line width=2,orange!50] (p-44) -- (p-42); \draw[line width=2,orange!50] (p-45) -- (p-43); \draw[line width=2,orange!50] (p-45) -- (p-44); \draw[line width=2,orange!50] (p-70) -- (p-41); \draw[line width=2,orange!50] (p-70) -- (p-43); \draw[line width=2,orange!50] (p-70) -- (p-71); \draw[line width=2,orange!50] (p-71) -- (p-43); \draw[line width=2,orange!50] (p-71) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 3 (purple): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/5.57, 64/1.20/5.19, 65/0.99/3.47, 66/1.59/4.27, 67/0.60/4.39, 68/0.00/3.58, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-65); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,purple!50] (p-16) -- (p-15); \draw[line width=2,purple!50] (p-17) -- (p-15); \draw[line width=2,purple!50] (p-17) -- (p-16); \draw[line width=2,purple!50] (p-18) -- (p-17); \draw[line width=2,purple!50] (p-19) -- (p-17); \draw[line width=2,purple!50] (p-19) -- (p-18); \draw[line width=2,purple!50] (p-20) -- (p-18); \draw[line width=2,purple!50] (p-21) -- (p-19); \draw[line width=2,purple!50] (p-21) -- (p-20); \draw[line width=2,purple!50] (p-22) -- (p-21); \draw[line width=2,purple!50] (p-23) -- (p-21); \draw[line width=2,purple!50] (p-24) -- (p-22); \draw[line width=2,purple!50] (p-25) -- (p-23); \draw[line width=2,purple!50] (p-25) -- (p-24); \draw[line width=2,purple!50] (p-26) -- (p-25); \draw[line width=2,purple!50] (p-27) -- (p-25); \draw[line width=2,purple!50] (p-28) -- (p-26); \draw[line width=2,purple!50] (p-29) -- (p-27); \draw[line width=2,purple!50] (p-29) -- (p-28); \draw[line width=2,purple!50] (p-30) -- (p-29); \draw[line width=2,purple!50] (p-31) -- (p-29); \draw[line width=2,purple!50] (p-32) -- (p-30); \draw[line width=2,purple!50] (p-33) -- (p-31); \draw[line width=2,purple!50] (p-33) -- (p-32); \draw[line width=2,purple!50] (p-34) -- (p-33); \draw[line width=2,purple!50] (p-35) -- (p-33); \draw[line width=2,purple!50] (p-36) -- (p-34); \draw[line width=2,purple!50] (p-37) -- (p-35); \draw[line width=2,purple!50] (p-37) -- (p-36); \draw[line width=2,purple!50] (p-38) -- (p-37); \draw[line width=2,purple!50] (p-39) -- (p-37); \draw[line width=2,purple!50] (p-40) -- (p-39); \draw[line width=2,purple!50] (p-40) -- (p-38); \draw[line width=2,purple!50] (p-41) -- (p-40); \draw[line width=2,purple!50] (p-42) -- (p-41); \draw[line width=2,purple!50] (p-43) -- (p-41); \draw[line width=2,purple!50] (p-43) -- (p-42); \draw[line width=2,purple!50] (p-49) -- (p-18); \draw[line width=2,purple!50] (p-49) -- (p-16); \draw[line width=2,purple!50] (p-49) -- (p-50); \draw[line width=2,purple!50] (p-50) -- (p-22); \draw[line width=2,purple!50] (p-50) -- (p-20); \draw[line width=2,purple!50] (p-50) -- (p-51); \draw[line width=2,purple!50] (p-51) -- (p-26); \draw[line width=2,purple!50] (p-51) -- (p-24); \draw[line width=2,purple!50] (p-51) -- (p-52); \draw[line width=2,purple!50] (p-52) -- (p-30); \draw[line width=2,purple!50] (p-52) -- (p-28); \draw[line width=2,purple!50] (p-52) -- (p-53); \draw[line width=2,purple!50] (p-53) -- (p-34); \draw[line width=2,purple!50] (p-53) -- (p-32); \draw[line width=2,purple!50] (p-53) -- (p-54); \draw[line width=2,purple!50] (p-54) -- (p-38); \draw[line width=2,purple!50] (p-54) -- (p-36); \draw[line width=2,purple!50] (p-54) -- (p-55); \draw[line width=2,purple!50] (p-55) -- (p-42); \draw[line width=2,purple!50] (p-55) -- (p-40); \draw[line width=2,purple!50] (p-61) -- (p-15); \draw[line width=2,purple!50] (p-61) -- (p-17); \draw[line width=2,purple!50] (p-61) -- (p-66); \draw[line width=2,purple!50] (p-62) -- (p-17); \draw[line width=2,purple!50] (p-62) -- (p-19); \draw[line width=2,purple!50] (p-62) -- (p-63); \draw[line width=2,purple!50] (p-63) -- (p-19); \draw[line width=2,purple!50] (p-64) -- (p-62); \draw[line width=2,purple!50] (p-64) -- (p-63); \draw[line width=2,purple!50] (p-64) -- (p-66); \draw[line width=2,purple!50] (p-69) -- (p-39); \draw[line width=2,purple!50] (p-69) -- (p-41); \draw[line width=2,purple!50] (p-70) -- (p-41); \draw[line width=2,purple!50] (p-70) -- (p-43); \draw[line width=2,purple!50] (p-70) -- (p-71); \draw[line width=2,purple!50] (p-71) -- (p-43); \draw[line width=2,purple!50] (p-72) -- (p-70); \draw[line width=2,purple!50] (p-72) -- (p-71); \draw[line width=2,purple!50] (p-72) -- (p-74); \draw[line width=2,purple!50] (p-74) -- (p-69); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 4 (hellgrau): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/5.57, 64/1.20/5.19, 65/0.99/3.47, 66/1.59/4.27, 67/0.60/4.39, 68/0.00/3.58, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-65); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,darkgray!50] (p-2) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-1); \draw[line width=2,darkgray!50] (p-4) -- (p-3); \draw[line width=2,darkgray!50] (p-5) -- (p-4); \draw[line width=2,darkgray!50] (p-5) -- (p-2); \draw[line width=2,darkgray!50] (p-6) -- (p-1); \draw[line width=2,darkgray!50] (p-8) -- (p-6); \draw[line width=2,darkgray!50] (p-9) -- (p-8); \draw[line width=2,darkgray!50] (p-10) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-9); \draw[line width=2,darkgray!50] (p-12) -- (p-10); \draw[line width=2,darkgray!50] (p-13) -- (p-11); \draw[line width=2,darkgray!50] (p-13) -- (p-12); \draw[line width=2,darkgray!50] (p-14) -- (p-13); \draw[line width=2,darkgray!50] (p-16) -- (p-14); \draw[line width=2,darkgray!50] (p-17) -- (p-16); \draw[line width=2,darkgray!50] (p-18) -- (p-17); \draw[line width=2,darkgray!50] (p-19) -- (p-17); \draw[line width=2,darkgray!50] (p-20) -- (p-18); \draw[line width=2,darkgray!50] (p-21) -- (p-19); \draw[line width=2,darkgray!50] (p-21) -- (p-20); \draw[line width=2,darkgray!50] (p-22) -- (p-21); \draw[line width=2,darkgray!50] (p-24) -- (p-22); \draw[line width=2,darkgray!50] (p-25) -- (p-24); \draw[line width=2,darkgray!50] (p-26) -- (p-25); \draw[line width=2,darkgray!50] (p-27) -- (p-25); \draw[line width=2,darkgray!50] (p-28) -- (p-26); \draw[line width=2,darkgray!50] (p-29) -- (p-27); \draw[line width=2,darkgray!50] (p-29) -- (p-28); \draw[line width=2,darkgray!50] (p-30) -- (p-29); \draw[line width=2,darkgray!50] (p-32) -- (p-30); \draw[line width=2,darkgray!50] (p-33) -- (p-32); \draw[line width=2,darkgray!50] (p-34) -- (p-33); \draw[line width=2,darkgray!50] (p-35) -- (p-33); \draw[line width=2,darkgray!50] (p-36) -- (p-34); \draw[line width=2,darkgray!50] (p-37) -- (p-35); \draw[line width=2,darkgray!50] (p-37) -- (p-36); \draw[line width=2,darkgray!50] (p-38) -- (p-37); \draw[line width=2,darkgray!50] (p-40) -- (p-38); \draw[line width=2,darkgray!50] (p-41) -- (p-40); \draw[line width=2,darkgray!50] (p-42) -- (p-41); \draw[line width=2,darkgray!50] (p-43) -- (p-41); \draw[line width=2,darkgray!50] (p-44) -- (p-42); \draw[line width=2,darkgray!50] (p-45) -- (p-43); \draw[line width=2,darkgray!50] (p-45) -- (p-44); \draw[line width=2,darkgray!50] (p-45) -- (p-59); \draw[line width=2,darkgray!50] (p-46) -- (p-6); \draw[line width=2,darkgray!50] (p-46) -- (p-3); \draw[line width=2,darkgray!50] (p-46) -- (p-47); \draw[line width=2,darkgray!50] (p-47) -- (p-10); \draw[line width=2,darkgray!50] (p-47) -- (p-8); \draw[line width=2,darkgray!50] (p-48) -- (p-14); \draw[line width=2,darkgray!50] (p-48) -- (p-12); \draw[line width=2,darkgray!50] (p-48) -- (p-49); \draw[line width=2,darkgray!50] (p-49) -- (p-18); \draw[line width=2,darkgray!50] (p-49) -- (p-16); \draw[line width=2,darkgray!50] (p-50) -- (p-22); \draw[line width=2,darkgray!50] (p-50) -- (p-20); \draw[line width=2,darkgray!50] (p-50) -- (p-51); \draw[line width=2,darkgray!50] (p-51) -- (p-26); \draw[line width=2,darkgray!50] (p-51) -- (p-24); \draw[line width=2,darkgray!50] (p-52) -- (p-30); \draw[line width=2,darkgray!50] (p-52) -- (p-28); \draw[line width=2,darkgray!50] (p-52) -- (p-53); \draw[line width=2,darkgray!50] (p-53) -- (p-34); \draw[line width=2,darkgray!50] (p-53) -- (p-32); \draw[line width=2,darkgray!50] (p-54) -- (p-38); \draw[line width=2,darkgray!50] (p-54) -- (p-36); \draw[line width=2,darkgray!50] (p-54) -- (p-55); \draw[line width=2,darkgray!50] (p-55) -- (p-42); \draw[line width=2,darkgray!50] (p-55) -- (p-40); \draw[line width=2,darkgray!50] (p-56) -- (p-4); \draw[line width=2,darkgray!50] (p-57) -- (p-56); \draw[line width=2,darkgray!50] (p-57) -- (p-5); \draw[line width=2,darkgray!50] (p-59) -- (p-57); \draw[line width=2,darkgray!50] (p-59) -- (p-60); \draw[line width=2,darkgray!50] (p-60) -- (p-44); \draw[line width=2,darkgray!50] (p-60) -- (p-56); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 5 (rot): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/5.57, 64/1.20/5.19, 65/0.99/3.47, 66/1.59/4.27, 67/0.60/4.39, 68/0.00/3.58, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-65); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,red!50] (p-2) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-2); \draw[line width=2,red!50] (p-4) -- (p-3); \draw[line width=2,red!50] (p-4) -- (p-2); \draw[line width=2,red!50] (p-5) -- (p-4); \draw[line width=2,red!50] (p-5) -- (p-2); \draw[line width=2,red!50] (p-6) -- (p-1); \draw[line width=2,red!50] (p-7) -- (p-1); \draw[line width=2,red!50] (p-7) -- (p-6); \draw[line width=2,red!50] (p-8) -- (p-7); \draw[line width=2,red!50] (p-8) -- (p-6); \draw[line width=2,red!50] (p-9) -- (p-7); \draw[line width=2,red!50] (p-9) -- (p-8); \draw[line width=2,red!50] (p-10) -- (p-9); \draw[line width=2,red!50] (p-11) -- (p-9); \draw[line width=2,red!50] (p-11) -- (p-10); \draw[line width=2,red!50] (p-12) -- (p-11); \draw[line width=2,red!50] (p-12) -- (p-10); \draw[line width=2,red!50] (p-13) -- (p-11); \draw[line width=2,red!50] (p-13) -- (p-12); \draw[line width=2,red!50] (p-14) -- (p-13); \draw[line width=2,red!50] (p-15) -- (p-13); \draw[line width=2,red!50] (p-15) -- (p-14); \draw[line width=2,red!50] (p-16) -- (p-15); \draw[line width=2,red!50] (p-16) -- (p-14); \draw[line width=2,red!50] (p-17) -- (p-15); \draw[line width=2,red!50] (p-17) -- (p-16); \draw[line width=2,red!50] (p-18) -- (p-17); \draw[line width=2,red!50] (p-19) -- (p-17); \draw[line width=2,red!50] (p-19) -- (p-18); \draw[line width=2,red!50] (p-20) -- (p-19); \draw[line width=2,red!50] (p-20) -- (p-18); \draw[line width=2,red!50] (p-21) -- (p-19); \draw[line width=2,red!50] (p-21) -- (p-20); \draw[line width=2,red!50] (p-23) -- (p-21); \draw[line width=2,red!50] (p-25) -- (p-23); \draw[line width=2,red!50] (p-26) -- (p-25); \draw[line width=2,red!50] (p-27) -- (p-25); \draw[line width=2,red!50] (p-27) -- (p-26); \draw[line width=2,red!50] (p-28) -- (p-27); \draw[line width=2,red!50] (p-28) -- (p-26); \draw[line width=2,red!50] (p-29) -- (p-27); \draw[line width=2,red!50] (p-29) -- (p-28); \draw[line width=2,red!50] (p-30) -- (p-29); \draw[line width=2,red!50] (p-31) -- (p-29); \draw[line width=2,red!50] (p-31) -- (p-30); \draw[line width=2,red!50] (p-32) -- (p-31); \draw[line width=2,red!50] (p-32) -- (p-30); \draw[line width=2,red!50] (p-33) -- (p-31); \draw[line width=2,red!50] (p-33) -- (p-32); \draw[line width=2,red!50] (p-34) -- (p-33); \draw[line width=2,red!50] (p-35) -- (p-33); \draw[line width=2,red!50] (p-35) -- (p-34); \draw[line width=2,red!50] (p-36) -- (p-35); \draw[line width=2,red!50] (p-36) -- (p-34); \draw[line width=2,red!50] (p-37) -- (p-35); \draw[line width=2,red!50] (p-37) -- (p-36); \draw[line width=2,red!50] (p-38) -- (p-37); \draw[line width=2,red!50] (p-39) -- (p-37); \draw[line width=2,red!50] (p-39) -- (p-38); \draw[line width=2,red!50] (p-40) -- (p-39); \draw[line width=2,red!50] (p-40) -- (p-38); \draw[line width=2,red!50] (p-41) -- (p-39); \draw[line width=2,red!50] (p-41) -- (p-40); \draw[line width=2,red!50] (p-42) -- (p-41); \draw[line width=2,red!50] (p-43) -- (p-41); \draw[line width=2,red!50] (p-43) -- (p-42); \draw[line width=2,red!50] (p-44) -- (p-43); \draw[line width=2,red!50] (p-44) -- (p-42); \draw[line width=2,red!50] (p-45) -- (p-43); \draw[line width=2,red!50] (p-45) -- (p-44); \draw[line width=2,red!50] (p-46) -- (p-6); \draw[line width=2,red!50] (p-46) -- (p-3); \draw[line width=2,red!50] (p-46) -- (p-47); \draw[line width=2,red!50] (p-47) -- (p-10); \draw[line width=2,red!50] (p-47) -- (p-8); \draw[line width=2,red!50] (p-47) -- (p-48); \draw[line width=2,red!50] (p-48) -- (p-14); \draw[line width=2,red!50] (p-48) -- (p-12); \draw[line width=2,red!50] (p-48) -- (p-49); \draw[line width=2,red!50] (p-49) -- (p-18); \draw[line width=2,red!50] (p-49) -- (p-16); \draw[line width=2,red!50] (p-49) -- (p-50); \draw[line width=2,red!50] (p-50) -- (p-20); \draw[line width=2,red!50] (p-50) -- (p-51); \draw[line width=2,red!50] (p-51) -- (p-26); \draw[line width=2,red!50] (p-51) -- (p-52); \draw[line width=2,red!50] (p-52) -- (p-30); \draw[line width=2,red!50] (p-52) -- (p-28); \draw[line width=2,red!50] (p-52) -- (p-53); \draw[line width=2,red!50] (p-53) -- (p-34); \draw[line width=2,red!50] (p-53) -- (p-32); \draw[line width=2,red!50] (p-53) -- (p-54); \draw[line width=2,red!50] (p-54) -- (p-38); \draw[line width=2,red!50] (p-54) -- (p-36); \draw[line width=2,red!50] (p-54) -- (p-55); \draw[line width=2,red!50] (p-55) -- (p-42); \draw[line width=2,red!50] (p-55) -- (p-40); \draw[line width=2,red!50] (p-58) -- (p-5); \draw[line width=2,red!50] (p-58) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 6 (violet): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/5.57, 64/1.20/5.19, 65/0.99/3.47, 66/1.59/4.27, 67/0.60/4.39, 68/0.00/3.58, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-65); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,violet!50] (p-18) -- (p-17); \draw[line width=2,violet!50] (p-19) -- (p-17); \draw[line width=2,violet!50] (p-19) -- (p-18); \draw[line width=2,violet!50] (p-20) -- (p-19); \draw[line width=2,violet!50] (p-20) -- (p-18); \draw[line width=2,violet!50] (p-21) -- (p-19); \draw[line width=2,violet!50] (p-21) -- (p-20); \draw[line width=2,violet!50] (p-62) -- (p-17); \draw[line width=2,violet!50] (p-62) -- (p-19); \draw[line width=2,violet!50] (p-62) -- (p-63); \draw[line width=2,violet!50] (p-63) -- (p-19); \draw[line width=2,violet!50] (p-63) -- (p-21); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 7 (teal) $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/5.57, 64/1.20/5.19, 65/0.99/3.47, 66/1.59/4.27, 67/0.60/4.39, 68/0.00/3.58, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-65); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,teal!50] (p-2) -- (p-1); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[line width=2,teal!50] (p-3) -- (p-1); \draw[line width=2,teal!50] (p-3) -- (p-2); \draw[line width=2,teal!50] (p-4) -- (p-3); \draw[line width=2,teal!50] (p-4) -- (p-2); \draw[line width=2,teal!50] (p-5) -- (p-4); \draw[line width=2,teal!50] (p-5) -- (p-2); \draw[line width=2,teal!50] (p-6) -- (p-1); \draw[line width=2,teal!50] (p-7) -- (p-1); \draw[line width=2,teal!50] (p-8) -- (p-6); \draw[line width=2,teal!50] (p-9) -- (p-7); \draw[line width=2,teal!50] (p-9) -- (p-8); \draw[line width=2,teal!50] (p-10) -- (p-9); \draw[line width=2,teal!50] (p-11) -- (p-9); \draw[line width=2,teal!50] (p-11) -- (p-10); \draw[line width=2,teal!50] (p-12) -- (p-11); \draw[line width=2,teal!50] (p-12) -- (p-10); \draw[line width=2,teal!50] (p-13) -- (p-11); \draw[line width=2,teal!50] (p-13) -- (p-12); \draw[line width=2,teal!50] (p-14) -- (p-13); \draw[line width=2,teal!50] (p-15) -- (p-13); \draw[line width=2,teal!50] (p-15) -- (p-14); \draw[line width=2,teal!50] (p-16) -- (p-15); \draw[line width=2,teal!50] (p-16) -- (p-14); \draw[line width=2,teal!50] (p-17) -- (p-16); \draw[line width=2,teal!50] (p-18) -- (p-17); \draw[line width=2,teal!50] (p-19) -- (p-17); \draw[line width=2,teal!50] (p-19) -- (p-18); \draw[line width=2,teal!50] (p-20) -- (p-19); \draw[line width=2,teal!50] (p-20) -- (p-18); \draw[line width=2,teal!50] (p-21) -- (p-19); \draw[line width=2,teal!50] (p-21) -- (p-20); \draw[line width=2,teal!50] (p-22) -- (p-21); \draw[line width=2,teal!50] (p-23) -- (p-22); \draw[line width=2,teal!50] (p-24) -- (p-23); \draw[line width=2,teal!50] (p-24) -- (p-22); \draw[line width=2,teal!50] (p-25) -- (p-23); \draw[line width=2,teal!50] (p-25) -- (p-24); \draw[line width=2,teal!50] (p-26) -- (p-25); \draw[line width=2,teal!50] (p-27) -- (p-25); \draw[line width=2,teal!50] (p-27) -- (p-26); \draw[line width=2,teal!50] (p-28) -- (p-27); \draw[line width=2,teal!50] (p-28) -- (p-26); \draw[line width=2,teal!50] (p-29) -- (p-27); \draw[line width=2,teal!50] (p-29) -- (p-28); \draw[line width=2,teal!50] (p-30) -- (p-29); \draw[line width=2,teal!50] (p-31) -- (p-29); \draw[line width=2,teal!50] (p-32) -- (p-30); \draw[line width=2,teal!50] (p-33) -- (p-31); \draw[line width=2,teal!50] (p-33) -- (p-32); \draw[line width=2,teal!50] (p-34) -- (p-33); \draw[line width=2,teal!50] (p-35) -- (p-33); \draw[line width=2,teal!50] (p-35) -- (p-34); \draw[line width=2,teal!50] (p-36) -- (p-35); \draw[line width=2,teal!50] (p-36) -- (p-34); \draw[line width=2,teal!50] (p-37) -- (p-35); \draw[line width=2,teal!50] (p-37) -- (p-36); \draw[line width=2,teal!50] (p-38) -- (p-37); \draw[line width=2,teal!50] (p-39) -- (p-37); \draw[line width=2,teal!50] (p-39) -- (p-38); \draw[line width=2,teal!50] (p-40) -- (p-39); \draw[line width=2,teal!50] (p-40) -- (p-38); \draw[line width=2,teal!50] (p-41) -- (p-40); \draw[line width=2,teal!50] (p-42) -- (p-41); \draw[line width=2,teal!50] (p-43) -- (p-41); \draw[line width=2,teal!50] (p-43) -- (p-42); \draw[line width=2,teal!50] (p-44) -- (p-43); \draw[line width=2,teal!50] (p-44) -- (p-42); \draw[line width=2,teal!50] (p-45) -- (p-43); \draw[line width=2,teal!50] (p-45) -- (p-44); \draw[line width=2,teal!50] (p-45) -- (p-59); \draw[line width=2,teal!50] (p-46) -- (p-6); \draw[line width=2,teal!50] (p-46) -- (p-3); \draw[line width=2,teal!50] (p-46) -- (p-47); \draw[line width=2,teal!50] (p-47) -- (p-10); \draw[line width=2,teal!50] (p-47) -- (p-8); \draw[line width=2,teal!50] (p-47) -- (p-48); \draw[line width=2,teal!50] (p-48) -- (p-14); \draw[line width=2,teal!50] (p-48) -- (p-12); \draw[line width=2,teal!50] (p-48) -- (p-49); \draw[line width=2,teal!50] (p-49) -- (p-18); \draw[line width=2,teal!50] (p-49) -- (p-16); \draw[line width=2,teal!50] (p-50) -- (p-22); \draw[line width=2,teal!50] (p-50) -- (p-20); \draw[line width=2,teal!50] (p-50) -- (p-51); \draw[line width=2,teal!50] (p-51) -- (p-26); \draw[line width=2,teal!50] (p-51) -- (p-24); \draw[line width=2,teal!50] (p-51) -- (p-52); \draw[line width=2,teal!50] (p-52) -- (p-30); \draw[line width=2,teal!50] (p-52) -- (p-28); \draw[line width=2,teal!50] (p-52) -- (p-53); \draw[line width=2,teal!50] (p-53) -- (p-34); \draw[line width=2,teal!50] (p-53) -- (p-32); \draw[line width=2,teal!50] (p-53) -- (p-54); \draw[line width=2,teal!50] (p-54) -- (p-36); \draw[line width=2,teal!50] (p-54) -- (p-55); \draw[line width=2,teal!50] (p-55) -- (p-42); \draw[line width=2,teal!50] (p-55) -- (p-40); \draw[line width=2,teal!50] (p-56) -- (p-46); \draw[line width=2,teal!50] (p-56) -- (p-4); \draw[line width=2,teal!50] (p-57) -- (p-56); \draw[line width=2,teal!50] (p-57) -- (p-5); \draw[line width=2,teal!50] (p-58) -- (p-57); \draw[line width=2,teal!50] (p-58) -- (p-5); \draw[line width=2,teal!50] (p-59) -- (p-57); \draw[line width=2,teal!50] (p-59) -- (p-58); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Weil der Ausgangsgraph 108° rotationssymmetrisch ist, die Bereiche aber nicht (Bereich 3), das deute ich so: Die Gestalt und Lage der Bereiche ist abhängig davon, welche 7 Einsetzkanten man am Anfang festlegt. Da gibt es ja verschiedene Möglichkeiten. Wenn man beispielsweise die Einsetzkanten auch um 180° um den Mittelpunkt des Graphen rotiert, würde sich bestimmt als Bereich 3 ein Bereich in der unteren Hälfte des Graphen ergeben. Um ein System in den Bereichen zu erkennen, müsste man also alle möglichen Anfangsmengen für Einsetzkanten zusammen betrachten. Ich halte es für möglich, dass man diese ganzen Varianten aus einer ersten Lösung kombinieren kann, so dass man nicht nochmal Button "acos(1/4)" starten muss.


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2387, eingetragen 2022-05-08

Haha, ich meinte den kite verschieben und den bürzel oben lassen... Ist aber egal, wir haben ja genug neues zum nachdenken... schönen Sonntag noch Haribo


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4173
Wohnort: Raun
  Beitrag No.2388, eingetragen 2022-05-08

Ich wills nochmal so formulieren: Bereich 1 ist nicht dadurch bestimmt, dass P55-P60 als Einsetzkante bestimmt wurde, sondern dadurch, dass P55-P60 als Einsetzkante bestimmt wurde und die ebenfalls als Einsatzkanten verwendbaren Kanten P45-P71, P69-P74, P56-P60, P45-P58, P21-P63, P58-P59 aus dem Graph entfernt wurden. So entstehen nochmal -zig Möglichkeiten, zu Kante P55-P60 einen Bereich zu bestimmen. Anstelle P45-P71, P69-P74, P56-P60, P45-P58, P21-P63, P58-P59 könnten auch viele andere Kanten entfernt werden. Es müssen nur Einsetzkanten sein, vermutlich auch dann noch, nachdem bereits paar Kanten entfernt wurden. [Die Antwort wurde nach Beitrag No.2386 begonnen.]


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4173
Wohnort: Raun
  Beitrag No.2389, eingetragen 2022-05-08

Ohren spitzen ist dann Kite von P13 nach P19. 76 Knoten, 2×Grad 2, 66×Grad 4, 4×Grad 5, 4×Grad 6, 0 Überschneidungen, 156 Kanten, minimal 0.99999999999999678035, maximal 1.00000000000000444089, Einsetzkanten=Beweglichkeit+7, einzustellende Kanten, Abstände und Winkel: $ %Eingabe war: % %Fig.1d 4-regular matchstick graph with 60 vertices. This graph is flexible. % % % % %P[1]=[88.77040952594916,-44.677831990038186]; P[2]=[135.0511491964971,-25.754483038360235]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2,blue_angle,2,60-blue_angle,2); N(46,6,3); N(47,10,8); N(48,14,12); N(49,18,16); N(50,22,20); N(51,26,24); N(52,30,28); N(53,34,32); N(54,38,36); N(55,42,40); N(56,46,4); N(57,56,5); L(58,57,5); L(59,57,58); N(60,44,55); A(58,45,Bew(5)); A(45,59,Bew(6)); A(59,60,Bew(6)); A(46,47,Bew(6)); A(47,48,Bew(6)); A(48,49,Bew(6)); A(49,50,Bew(6)); A(50,51,Bew(6)); A(51,52,Bew(6)); A(52,53,Bew(6)); A(53,54,Bew(6)); A(54,55,Bew(6)); A(60,56,Bew(6)); % %L(61,15,17); L(62,17,19); L(63,13,15); A(63,61); L(64,63,61); Q(65,64,62,ab(61,13,15,63,64),ab(1,2)); A(62,66); % %L(69,39,41); L(70,41,43); L(71,43,45); A(70,71); L(72,70,71); Q(73,69,72,ab(1,2),ab(70,45,43,71,72)); A(74,69); % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/2.36, 64/1.20/2.74, 65/0.99/4.46, 66/1.59/3.66, 67/0.60/3.54, 68/0.00/4.34, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/82.24/97.76/0.4/Blue, 13/22.24/37.76/0.4/Blue, 21/322.24/337.76/0.4/Blue, 29/262.24/277.76/0.4/Blue, 37/202.24/217.76/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 15/13, 15/14, 16/15, 16/14, 17/15, 17/16, 18/17, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 27/25, 27/26, 28/27, 28/26, 29/27, 29/28, 30/29, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/33, 35/33, 35/34, 36/35, 36/34, 37/35, 37/36, 38/37, 39/37, 39/38, 40/39, 40/38, 41/39, 41/40, 42/41, 43/41, 43/42, 44/43, 44/42, 45/43, 45/44, 45/59, 46/6, 46/3, 46/47, 47/10, 47/8, 47/48, 48/14, 48/12, 48/49, 49/18, 49/16, 49/50, 50/22, 50/20, 50/51, 51/26, 51/24, 51/52, 52/30, 52/28, 52/53, 53/34, 53/32, 53/54, 54/38, 54/36, 54/55, 55/42, 55/40, 56/46, 56/4, 57/56, 57/5, 58/57, 58/5, 58/45, 59/57, 59/58, 59/60, 60/44, 60/55, 60/56, 61/15, 61/17, 62/17, 62/19, 62/66, 63/13, 63/15, 63/61, 64/63, 64/61, 65/66, 65/62, 66/64, 67/64, 67/66, 67/65, 68/65, 68/67, 69/39, 69/41, 70/41, 70/43, 70/71, 71/43, 71/45, 72/70, 72/71, 72/74, 73/69, 73/74, 73/75, 74/69, 75/74, 75/72, 76/73, 76/75} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,76} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/82.24/97.76/0.4/Blue, 13/22.24/37.76/0.4/Blue, 21/322.24/337.76/0.4/Blue, 29/262.24/277.76/0.4/Blue, 37/202.24/217.76/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/308, 2/352, 3/172, 4/52, 5/352, 6/8, 7/188, 8/128, 9/188, 10/352, 11/172, 12/52, 13/308, 14/8, 15/68, 16/8, 17/68, 18/352, 19/52, 20/352, 21/188, 22/248, 23/128, 24/8, 25/68, 26/232, 27/52, 28/292, 29/52, 30/248, 31/8, 32/248, 33/8, 34/232, 35/52, 36/232, 37/352, 38/188, 39/8, 40/188, 41/52, 42/172, 43/52, 44/232, 45/8, 46/32, 47/2, 48/332, 49/302, 50/272, 51/242, 52/333, 53/182, 54/152, 55/243, 56/182, 57/128, 58/308, 59/68, 60/213, 61/68, 62/37, 63/248, 64/277, 65/97, 66/37, 67/277, 68/157, 69/143, 70/112, 71/292, 72/263, 73/23, 74/143, 75/323, 76/23} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Button "acos(1/4)" wählt P45-P58, P45-P71, P69-P74, P58-P59, P56-P60, P61-P63, P55-P60 als Einsetzkanten. Der Graph ist wieder symmetrisch, die Bereiche der Einsetzkanten sind es nicht immer. Bereich 1 (hellblau) $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/2.36, 64/1.20/2.74, 65/0.99/4.46, 66/1.59/3.66, 67/0.60/3.54, 68/0.00/4.34, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-67); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-2) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-2); \draw[line width=2,blue!50] (p-4) -- (p-3); \draw[line width=2,blue!50] (p-4) -- (p-2); \draw[line width=2,blue!50] (p-5) -- (p-4); \draw[line width=2,blue!50] (p-5) -- (p-2); \draw[line width=2,blue!50] (p-6) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-6); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-6); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-8); \draw[line width=2,blue!50] (p-10) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-12) -- (p-11); \draw[line width=2,blue!50] (p-12) -- (p-10); \draw[line width=2,blue!50] (p-13) -- (p-11); \draw[line width=2,blue!50] (p-13) -- (p-12); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-14); \draw[line width=2,blue!50] (p-16) -- (p-15); \draw[line width=2,blue!50] (p-16) -- (p-14); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-18) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-19); \draw[line width=2,blue!50] (p-20) -- (p-18); \draw[line width=2,blue!50] (p-21) -- (p-19); \draw[line width=2,blue!50] (p-21) -- (p-20); \draw[line width=2,blue!50] (p-23) -- (p-21); \draw[line width=2,blue!50] (p-25) -- (p-23); \draw[line width=2,blue!50] (p-26) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-26); \draw[line width=2,blue!50] (p-28) -- (p-27); \draw[line width=2,blue!50] (p-28) -- (p-26); \draw[line width=2,blue!50] (p-29) -- (p-27); \draw[line width=2,blue!50] (p-29) -- (p-28); \draw[line width=2,blue!50] (p-30) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-30); \draw[line width=2,blue!50] (p-32) -- (p-31); \draw[line width=2,blue!50] (p-32) -- (p-30); \draw[line width=2,blue!50] (p-33) -- (p-31); \draw[line width=2,blue!50] (p-33) -- (p-32); \draw[line width=2,blue!50] (p-34) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-34); \draw[line width=2,blue!50] (p-36) -- (p-35); \draw[line width=2,blue!50] (p-36) -- (p-34); \draw[line width=2,blue!50] (p-37) -- (p-35); \draw[line width=2,blue!50] (p-37) -- (p-36); \draw[line width=2,blue!50] (p-38) -- (p-37); \draw[line width=2,blue!50] (p-39) -- (p-37); \draw[line width=2,blue!50] (p-39) -- (p-38); \draw[line width=2,blue!50] (p-40) -- (p-39); \draw[line width=2,blue!50] (p-40) -- (p-38); \draw[line width=2,blue!50] (p-41) -- (p-39); \draw[line width=2,blue!50] (p-41) -- (p-40); \draw[line width=2,blue!50] (p-42) -- (p-41); \draw[line width=2,blue!50] (p-43) -- (p-41); \draw[line width=2,blue!50] (p-43) -- (p-42); \draw[line width=2,blue!50] (p-44) -- (p-43); \draw[line width=2,blue!50] (p-44) -- (p-42); \draw[line width=2,blue!50] (p-45) -- (p-43); \draw[line width=2,blue!50] (p-45) -- (p-44); \draw[line width=2,blue!50] (p-46) -- (p-6); \draw[line width=2,blue!50] (p-46) -- (p-3); \draw[line width=2,blue!50] (p-46) -- (p-47); \draw[line width=2,blue!50] (p-47) -- (p-10); \draw[line width=2,blue!50] (p-47) -- (p-8); \draw[line width=2,blue!50] (p-47) -- (p-48); \draw[line width=2,blue!50] (p-48) -- (p-14); \draw[line width=2,blue!50] (p-48) -- (p-12); \draw[line width=2,blue!50] (p-48) -- (p-49); \draw[line width=2,blue!50] (p-49) -- (p-18); \draw[line width=2,blue!50] (p-49) -- (p-16); \draw[line width=2,blue!50] (p-49) -- (p-50); \draw[line width=2,blue!50] (p-50) -- (p-20); \draw[line width=2,blue!50] (p-50) -- (p-51); \draw[line width=2,blue!50] (p-51) -- (p-26); \draw[line width=2,blue!50] (p-51) -- (p-52); \draw[line width=2,blue!50] (p-52) -- (p-30); \draw[line width=2,blue!50] (p-52) -- (p-28); \draw[line width=2,blue!50] (p-52) -- (p-53); \draw[line width=2,blue!50] (p-53) -- (p-34); \draw[line width=2,blue!50] (p-53) -- (p-32); \draw[line width=2,blue!50] (p-53) -- (p-54); \draw[line width=2,blue!50] (p-54) -- (p-38); \draw[line width=2,blue!50] (p-54) -- (p-36); \draw[line width=2,blue!50] (p-54) -- (p-55); \draw[line width=2,blue!50] (p-55) -- (p-42); \draw[line width=2,blue!50] (p-55) -- (p-40); \draw[line width=2,blue!50] (p-58) -- (p-5); \draw[line width=2,blue!50] (p-58) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 2 (orange): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/2.36, 64/1.20/2.74, 65/0.99/4.46, 66/1.59/3.66, 67/0.60/3.54, 68/0.00/4.34, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-67); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,orange!50] (p-42) -- (p-41); \draw[line width=2,orange!50] (p-43) -- (p-41); \draw[line width=2,orange!50] (p-43) -- (p-42); \draw[line width=2,orange!50] (p-44) -- (p-43); \draw[line width=2,orange!50] (p-44) -- (p-42); \draw[line width=2,orange!50] (p-45) -- (p-43); \draw[line width=2,orange!50] (p-45) -- (p-44); \draw[line width=2,orange!50] (p-70) -- (p-41); \draw[line width=2,orange!50] (p-70) -- (p-43); \draw[line width=2,orange!50] (p-70) -- (p-71); \draw[line width=2,orange!50] (p-71) -- (p-43); \draw[line width=2,orange!50] (p-71) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 3 (purple): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/2.36, 64/1.20/2.74, 65/0.99/4.46, 66/1.59/3.66, 67/0.60/3.54, 68/0.00/4.34, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-67); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,purple!50] (p-14) -- (p-13); \draw[line width=2,purple!50] (p-15) -- (p-13); \draw[line width=2,purple!50] (p-15) -- (p-14); \draw[line width=2,purple!50] (p-16) -- (p-15); \draw[line width=2,purple!50] (p-16) -- (p-14); \draw[line width=2,purple!50] (p-17) -- (p-15); \draw[line width=2,purple!50] (p-17) -- (p-16); \draw[line width=2,purple!50] (p-18) -- (p-17); \draw[line width=2,purple!50] (p-19) -- (p-18); \draw[line width=2,purple!50] (p-20) -- (p-18); \draw[line width=2,purple!50] (p-21) -- (p-19); \draw[line width=2,purple!50] (p-21) -- (p-20); \draw[line width=2,purple!50] (p-22) -- (p-21); \draw[line width=2,purple!50] (p-23) -- (p-21); \draw[line width=2,purple!50] (p-24) -- (p-22); \draw[line width=2,purple!50] (p-25) -- (p-23); \draw[line width=2,purple!50] (p-25) -- (p-24); \draw[line width=2,purple!50] (p-26) -- (p-25); \draw[line width=2,purple!50] (p-27) -- (p-25); \draw[line width=2,purple!50] (p-28) -- (p-26); \draw[line width=2,purple!50] (p-29) -- (p-27); \draw[line width=2,purple!50] (p-29) -- (p-28); \draw[line width=2,purple!50] (p-30) -- (p-29); \draw[line width=2,purple!50] (p-31) -- (p-29); \draw[line width=2,purple!50] (p-32) -- (p-30); \draw[line width=2,purple!50] (p-33) -- (p-31); \draw[line width=2,purple!50] (p-33) -- (p-32); \draw[line width=2,purple!50] (p-34) -- (p-33); \draw[line width=2,purple!50] (p-35) -- (p-33); \draw[line width=2,purple!50] (p-36) -- (p-34); \draw[line width=2,purple!50] (p-37) -- (p-35); \draw[line width=2,purple!50] (p-37) -- (p-36); \draw[line width=2,purple!50] (p-38) -- (p-37); \draw[line width=2,purple!50] (p-39) -- (p-37); \draw[line width=2,purple!50] (p-40) -- (p-39); \draw[line width=2,purple!50] (p-40) -- (p-38); \draw[line width=2,purple!50] (p-41) -- (p-40); \draw[line width=2,purple!50] (p-42) -- (p-41); \draw[line width=2,purple!50] (p-43) -- (p-41); \draw[line width=2,purple!50] (p-43) -- (p-42); \draw[line width=2,purple!50] (p-49) -- (p-18); \draw[line width=2,purple!50] (p-49) -- (p-16); \draw[line width=2,purple!50] (p-49) -- (p-50); \draw[line width=2,purple!50] (p-50) -- (p-22); \draw[line width=2,purple!50] (p-50) -- (p-20); \draw[line width=2,purple!50] (p-50) -- (p-51); \draw[line width=2,purple!50] (p-51) -- (p-26); \draw[line width=2,purple!50] (p-51) -- (p-24); \draw[line width=2,purple!50] (p-51) -- (p-52); \draw[line width=2,purple!50] (p-52) -- (p-30); \draw[line width=2,purple!50] (p-52) -- (p-28); \draw[line width=2,purple!50] (p-52) -- (p-53); \draw[line width=2,purple!50] (p-53) -- (p-34); \draw[line width=2,purple!50] (p-53) -- (p-32); \draw[line width=2,purple!50] (p-53) -- (p-54); \draw[line width=2,purple!50] (p-54) -- (p-38); \draw[line width=2,purple!50] (p-54) -- (p-36); \draw[line width=2,purple!50] (p-54) -- (p-55); \draw[line width=2,purple!50] (p-55) -- (p-42); \draw[line width=2,purple!50] (p-55) -- (p-40); \draw[line width=2,purple!50] (p-61) -- (p-17); \draw[line width=2,purple!50] (p-62) -- (p-17); \draw[line width=2,purple!50] (p-62) -- (p-19); \draw[line width=2,purple!50] (p-62) -- (p-66); \draw[line width=2,purple!50] (p-63) -- (p-13); \draw[line width=2,purple!50] (p-64) -- (p-63); \draw[line width=2,purple!50] (p-64) -- (p-61); \draw[line width=2,purple!50] (p-66) -- (p-64); \draw[line width=2,purple!50] (p-69) -- (p-39); \draw[line width=2,purple!50] (p-69) -- (p-41); \draw[line width=2,purple!50] (p-70) -- (p-41); \draw[line width=2,purple!50] (p-70) -- (p-43); \draw[line width=2,purple!50] (p-70) -- (p-71); \draw[line width=2,purple!50] (p-71) -- (p-43); \draw[line width=2,purple!50] (p-72) -- (p-70); \draw[line width=2,purple!50] (p-72) -- (p-71); \draw[line width=2,purple!50] (p-72) -- (p-74); \draw[line width=2,purple!50] (p-74) -- (p-69); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 4 (hellgrau): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/2.36, 64/1.20/2.74, 65/0.99/4.46, 66/1.59/3.66, 67/0.60/3.54, 68/0.00/4.34, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-67); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,darkgray!50] (p-2) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-2); \draw[line width=2,darkgray!50] (p-4) -- (p-3); \draw[line width=2,darkgray!50] (p-4) -- (p-2); \draw[line width=2,darkgray!50] (p-5) -- (p-4); \draw[line width=2,darkgray!50] (p-5) -- (p-2); \draw[line width=2,darkgray!50] (p-6) -- (p-1); \draw[line width=2,darkgray!50] (p-7) -- (p-1); \draw[line width=2,darkgray!50] (p-8) -- (p-6); \draw[line width=2,darkgray!50] (p-9) -- (p-7); \draw[line width=2,darkgray!50] (p-9) -- (p-8); \draw[line width=2,darkgray!50] (p-10) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-10); \draw[line width=2,darkgray!50] (p-12) -- (p-11); \draw[line width=2,darkgray!50] (p-12) -- (p-10); \draw[line width=2,darkgray!50] (p-13) -- (p-11); \draw[line width=2,darkgray!50] (p-13) -- (p-12); \draw[line width=2,darkgray!50] (p-14) -- (p-13); \draw[line width=2,darkgray!50] (p-15) -- (p-13); \draw[line width=2,darkgray!50] (p-15) -- (p-14); \draw[line width=2,darkgray!50] (p-16) -- (p-15); \draw[line width=2,darkgray!50] (p-16) -- (p-14); \draw[line width=2,darkgray!50] (p-17) -- (p-16); \draw[line width=2,darkgray!50] (p-18) -- (p-17); \draw[line width=2,darkgray!50] (p-19) -- (p-17); \draw[line width=2,darkgray!50] (p-19) -- (p-18); \draw[line width=2,darkgray!50] (p-20) -- (p-19); \draw[line width=2,darkgray!50] (p-20) -- (p-18); \draw[line width=2,darkgray!50] (p-21) -- (p-19); \draw[line width=2,darkgray!50] (p-21) -- (p-20); \draw[line width=2,darkgray!50] (p-22) -- (p-21); \draw[line width=2,darkgray!50] (p-23) -- (p-22); \draw[line width=2,darkgray!50] (p-24) -- (p-23); \draw[line width=2,darkgray!50] (p-24) -- (p-22); \draw[line width=2,darkgray!50] (p-25) -- (p-23); \draw[line width=2,darkgray!50] (p-25) -- (p-24); \draw[line width=2,darkgray!50] (p-26) -- (p-25); \draw[line width=2,darkgray!50] (p-27) -- (p-25); \draw[line width=2,darkgray!50] (p-27) -- (p-26); \draw[line width=2,darkgray!50] (p-28) -- (p-27); \draw[line width=2,darkgray!50] (p-28) -- (p-26); \draw[line width=2,darkgray!50] (p-29) -- (p-27); \draw[line width=2,darkgray!50] (p-29) -- (p-28); \draw[line width=2,darkgray!50] (p-30) -- (p-29); \draw[line width=2,darkgray!50] (p-31) -- (p-29); \draw[line width=2,darkgray!50] (p-32) -- (p-30); \draw[line width=2,darkgray!50] (p-33) -- (p-31); \draw[line width=2,darkgray!50] (p-33) -- (p-32); \draw[line width=2,darkgray!50] (p-34) -- (p-33); \draw[line width=2,darkgray!50] (p-35) -- (p-33); \draw[line width=2,darkgray!50] (p-35) -- (p-34); \draw[line width=2,darkgray!50] (p-36) -- (p-35); \draw[line width=2,darkgray!50] (p-36) -- (p-34); \draw[line width=2,darkgray!50] (p-37) -- (p-35); \draw[line width=2,darkgray!50] (p-37) -- (p-36); \draw[line width=2,darkgray!50] (p-38) -- (p-37); \draw[line width=2,darkgray!50] (p-39) -- (p-37); \draw[line width=2,darkgray!50] (p-39) -- (p-38); \draw[line width=2,darkgray!50] (p-40) -- (p-39); \draw[line width=2,darkgray!50] (p-40) -- (p-38); \draw[line width=2,darkgray!50] (p-41) -- (p-40); \draw[line width=2,darkgray!50] (p-42) -- (p-41); \draw[line width=2,darkgray!50] (p-43) -- (p-41); \draw[line width=2,darkgray!50] (p-43) -- (p-42); \draw[line width=2,darkgray!50] (p-44) -- (p-43); \draw[line width=2,darkgray!50] (p-44) -- (p-42); \draw[line width=2,darkgray!50] (p-45) -- (p-43); \draw[line width=2,darkgray!50] (p-45) -- (p-44); \draw[line width=2,darkgray!50] (p-45) -- (p-59); \draw[line width=2,darkgray!50] (p-46) -- (p-6); \draw[line width=2,darkgray!50] (p-46) -- (p-3); \draw[line width=2,darkgray!50] (p-46) -- (p-47); \draw[line width=2,darkgray!50] (p-47) -- (p-10); \draw[line width=2,darkgray!50] (p-47) -- (p-8); \draw[line width=2,darkgray!50] (p-47) -- (p-48); \draw[line width=2,darkgray!50] (p-48) -- (p-14); \draw[line width=2,darkgray!50] (p-48) -- (p-12); \draw[line width=2,darkgray!50] (p-48) -- (p-49); \draw[line width=2,darkgray!50] (p-49) -- (p-18); \draw[line width=2,darkgray!50] (p-49) -- (p-16); \draw[line width=2,darkgray!50] (p-50) -- (p-22); \draw[line width=2,darkgray!50] (p-50) -- (p-20); \draw[line width=2,darkgray!50] (p-50) -- (p-51); \draw[line width=2,darkgray!50] (p-51) -- (p-26); \draw[line width=2,darkgray!50] (p-51) -- (p-24); \draw[line width=2,darkgray!50] (p-51) -- (p-52); \draw[line width=2,darkgray!50] (p-52) -- (p-30); \draw[line width=2,darkgray!50] (p-52) -- (p-28); \draw[line width=2,darkgray!50] (p-52) -- (p-53); \draw[line width=2,darkgray!50] (p-53) -- (p-34); \draw[line width=2,darkgray!50] (p-53) -- (p-32); \draw[line width=2,darkgray!50] (p-53) -- (p-54); \draw[line width=2,darkgray!50] (p-54) -- (p-36); \draw[line width=2,darkgray!50] (p-54) -- (p-55); \draw[line width=2,darkgray!50] (p-55) -- (p-42); \draw[line width=2,darkgray!50] (p-55) -- (p-40); \draw[line width=2,darkgray!50] (p-56) -- (p-46); \draw[line width=2,darkgray!50] (p-56) -- (p-4); \draw[line width=2,darkgray!50] (p-57) -- (p-56); \draw[line width=2,darkgray!50] (p-57) -- (p-5); \draw[line width=2,darkgray!50] (p-58) -- (p-57); \draw[line width=2,darkgray!50] (p-58) -- (p-5); \draw[line width=2,darkgray!50] (p-59) -- (p-57); \draw[line width=2,darkgray!50] (p-59) -- (p-58); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 5 (rot): $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/2.36, 64/1.20/2.74, 65/0.99/4.46, 66/1.59/3.66, 67/0.60/3.54, 68/0.00/4.34, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-67); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,red!50] (p-2) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-1); \draw[line width=2,red!50] (p-4) -- (p-3); \draw[line width=2,red!50] (p-5) -- (p-4); \draw[line width=2,red!50] (p-5) -- (p-2); \draw[line width=2,red!50] (p-6) -- (p-1); \draw[line width=2,red!50] (p-8) -- (p-6); \draw[line width=2,red!50] (p-9) -- (p-8); \draw[line width=2,red!50] (p-10) -- (p-9); \draw[line width=2,red!50] (p-11) -- (p-9); \draw[line width=2,red!50] (p-12) -- (p-10); \draw[line width=2,red!50] (p-13) -- (p-11); \draw[line width=2,red!50] (p-13) -- (p-12); \draw[line width=2,red!50] (p-14) -- (p-13); \draw[line width=2,red!50] (p-16) -- (p-14); \draw[line width=2,red!50] (p-17) -- (p-16); \draw[line width=2,red!50] (p-18) -- (p-17); \draw[line width=2,red!50] (p-19) -- (p-17); \draw[line width=2,red!50] (p-20) -- (p-18); \draw[line width=2,red!50] (p-21) -- (p-19); \draw[line width=2,red!50] (p-21) -- (p-20); \draw[line width=2,red!50] (p-22) -- (p-21); \draw[line width=2,red!50] (p-24) -- (p-22); \draw[line width=2,red!50] (p-25) -- (p-24); \draw[line width=2,red!50] (p-26) -- (p-25); \draw[line width=2,red!50] (p-27) -- (p-25); \draw[line width=2,red!50] (p-28) -- (p-26); \draw[line width=2,red!50] (p-29) -- (p-27); \draw[line width=2,red!50] (p-29) -- (p-28); \draw[line width=2,red!50] (p-30) -- (p-29); \draw[line width=2,red!50] (p-32) -- (p-30); \draw[line width=2,red!50] (p-33) -- (p-32); \draw[line width=2,red!50] (p-34) -- (p-33); \draw[line width=2,red!50] (p-35) -- (p-33); \draw[line width=2,red!50] (p-36) -- (p-34); \draw[line width=2,red!50] (p-37) -- (p-35); \draw[line width=2,red!50] (p-37) -- (p-36); \draw[line width=2,red!50] (p-38) -- (p-37); \draw[line width=2,red!50] (p-40) -- (p-38); \draw[line width=2,red!50] (p-41) -- (p-40); \draw[line width=2,red!50] (p-42) -- (p-41); \draw[line width=2,red!50] (p-43) -- (p-41); \draw[line width=2,red!50] (p-44) -- (p-42); \draw[line width=2,red!50] (p-45) -- (p-43); \draw[line width=2,red!50] (p-45) -- (p-44); \draw[line width=2,red!50] (p-45) -- (p-59); \draw[line width=2,red!50] (p-46) -- (p-6); \draw[line width=2,red!50] (p-46) -- (p-3); \draw[line width=2,red!50] (p-46) -- (p-47); \draw[line width=2,red!50] (p-47) -- (p-10); \draw[line width=2,red!50] (p-47) -- (p-8); \draw[line width=2,red!50] (p-48) -- (p-14); \draw[line width=2,red!50] (p-48) -- (p-12); \draw[line width=2,red!50] (p-48) -- (p-49); \draw[line width=2,red!50] (p-49) -- (p-18); \draw[line width=2,red!50] (p-49) -- (p-16); \draw[line width=2,red!50] (p-50) -- (p-22); \draw[line width=2,red!50] (p-50) -- (p-20); \draw[line width=2,red!50] (p-50) -- (p-51); \draw[line width=2,red!50] (p-51) -- (p-26); \draw[line width=2,red!50] (p-51) -- (p-24); \draw[line width=2,red!50] (p-52) -- (p-30); \draw[line width=2,red!50] (p-52) -- (p-28); \draw[line width=2,red!50] (p-52) -- (p-53); \draw[line width=2,red!50] (p-53) -- (p-34); \draw[line width=2,red!50] (p-53) -- (p-32); \draw[line width=2,red!50] (p-54) -- (p-38); \draw[line width=2,red!50] (p-54) -- (p-36); \draw[line width=2,red!50] (p-54) -- (p-55); \draw[line width=2,red!50] (p-55) -- (p-42); \draw[line width=2,red!50] (p-55) -- (p-40); \draw[line width=2,red!50] (p-56) -- (p-4); \draw[line width=2,red!50] (p-57) -- (p-56); \draw[line width=2,red!50] (p-57) -- (p-5); \draw[line width=2,red!50] (p-59) -- (p-57); \draw[line width=2,red!50] (p-59) -- (p-60); \draw[line width=2,red!50] (p-60) -- (p-44); \draw[line width=2,red!50] (p-60) -- (p-56); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 6 (violet) $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/2.36, 64/1.20/2.74, 65/0.99/4.46, 66/1.59/3.66, 67/0.60/3.54, 68/0.00/4.34, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-67); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,violet!50] (p-14) -- (p-13); \draw[line width=2,violet!50] (p-15) -- (p-13); \draw[line width=2,violet!50] (p-15) -- (p-14); \draw[line width=2,violet!50] (p-16) -- (p-15); \draw[line width=2,violet!50] (p-16) -- (p-14); \draw[line width=2,violet!50] (p-17) -- (p-15); \draw[line width=2,violet!50] (p-17) -- (p-16); \draw[line width=2,violet!50] (p-61) -- (p-15); \draw[line width=2,violet!50] (p-61) -- (p-17); \draw[line width=2,violet!50] (p-63) -- (p-13); \draw[line width=2,violet!50] (p-63) -- (p-15); \draw[line width=2,violet!50] (p-63) -- (p-61); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Bereich 7 (teal) $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/6.48/0.00, 2/7.40/0.38, 3/6.61/0.99, 4/7.54/1.37, 5/8.33/0.76, 6/6.34/0.99, 7/5.55/0.38, 8/5.42/1.37, 9/4.63/0.76, 10/4.76/1.75, 11/3.84/1.37, 12/3.97/2.36, 13/3.05/1.98, 14/3.84/2.59, 15/2.91/2.97, 16/3.70/3.58, 17/2.78/3.96, 18/3.70/4.34, 19/2.91/4.95, 20/3.84/5.33, 21/3.05/5.95, 22/3.97/5.57, 23/3.84/6.56, 24/4.76/6.18, 25/4.63/7.17, 26/5.42/6.56, 27/5.55/7.55, 28/6.34/6.94, 29/6.48/7.93, 30/6.61/6.94, 31/7.40/7.55, 32/7.54/6.56, 33/8.33/7.17, 34/8.20/6.18, 35/9.12/6.56, 36/8.99/5.57, 37/9.91/5.95, 38/9.12/5.33, 39/10.05/4.95, 40/9.26/4.34, 41/10.18/3.96, 42/9.26/3.58, 43/10.05/2.97, 44/9.12/2.59, 45/9.91/1.98, 46/6.48/1.98, 47/5.55/2.36, 48/4.76/2.97, 49/4.63/3.96, 50/4.76/4.95, 51/5.55/5.57, 52/6.48/5.95, 53/7.40/5.57, 54/8.20/4.95, 55/8.33/3.96, 56/7.40/2.36, 57/8.20/1.75, 58/9.12/1.37, 59/8.99/2.36, 60/8.20/2.97, 61/1.99/3.35, 62/1.99/4.58, 63/2.12/2.36, 64/1.20/2.74, 65/0.99/4.46, 66/1.59/3.66, 67/0.60/3.54, 68/0.00/4.34, 69/10.97/4.58, 70/10.97/3.35, 71/10.84/2.36, 72/11.76/2.74, 73/11.97/4.46, 74/11.37/3.66, 75/12.36/3.54, 76/12.96/4.34} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[white] (p-68) -- (p-67); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,teal!50] (p-2) -- (p-1); \draw[line width=2,teal!50] (p-3) -- (p-1); \draw[line width=2,teal!50] (p-3) -- (p-2); \draw[line width=2,teal!50] (p-4) -- (p-3); \draw[line width=2,teal!50] (p-4) -- (p-2); \draw[line width=2,teal!50] (p-5) -- (p-4); \draw[line width=2,teal!50] (p-5) -- (p-2); \draw[line width=2,teal!50] (p-6) -- (p-1); \draw[line width=2,teal!50] (p-7) -- (p-6); \draw[line width=2,teal!50] (p-8) -- (p-7); \draw[line width=2,teal!50] (p-8) -- (p-6); \draw[line width=2,teal!50] (p-9) -- (p-7); \draw[line width=2,teal!50] (p-9) -- (p-8); \draw[line width=2,teal!50] (p-10) -- (p-9); \draw[line width=2,teal!50] (p-11) -- (p-9); \draw[line width=2,teal!50] (p-11) -- (p-10); \draw[line width=2,teal!50] (p-12) -- (p-11); \draw[line width=2,teal!50] (p-12) -- (p-10); \draw[line width=2,teal!50] (p-13) -- (p-11); \draw[line width=2,teal!50] (p-13) -- (p-12); \draw[line width=2,teal!50] (p-14) -- (p-13); \draw[line width=2,teal!50] (p-15) -- (p-13); \draw[line width=2,teal!50] (p-15) -- (p-14); \draw[line width=2,teal!50] (p-16) -- (p-15); \draw[line width=2,teal!50] (p-16) -- (p-14); \draw[line width=2,teal!50] (p-17) -- (p-15); \draw[line width=2,teal!50] (p-17) -- (p-16); \draw[line width=2,teal!50] (p-18) -- (p-17); \draw[line width=2,teal!50] (p-19) -- (p-17); \draw[line width=2,teal!50] (p-19) -- (p-18); \draw[line width=2,teal!50] (p-20) -- (p-19); \draw[line width=2,teal!50] (p-20) -- (p-18); \draw[line width=2,teal!50] (p-21) -- (p-19); \draw[line width=2,teal!50] (p-21) -- (p-20); \draw[line width=2,teal!50] (p-22) -- (p-21); \draw[line width=2,teal!50] (p-23) -- (p-21); \draw[line width=2,teal!50] (p-24) -- (p-22); \draw[line width=2,teal!50] (p-25) -- (p-23); \draw[line width=2,teal!50] (p-25) -- (p-24); \draw[line width=2,teal!50] (p-26) -- (p-25); \draw[line width=2,teal!50] (p-27) -- (p-25); \draw[line width=2,teal!50] (p-27) -- (p-26); \draw[line width=2,teal!50] (p-28) -- (p-27); \draw[line width=2,teal!50] (p-28) -- (p-26); \draw[line width=2,teal!50] (p-29) -- (p-27); \draw[line width=2,teal!50] (p-29) -- (p-28); \draw[line width=2,teal!50] (p-30) -- (p-29); \draw[line width=2,teal!50] (p-31) -- (p-29); \draw[line width=2,teal!50] (p-31) -- (p-30); \draw[line width=2,teal!50] (p-32) -- (p-31); \draw[line width=2,teal!50] (p-32) -- (p-30); \draw[line width=2,teal!50] (p-33) -- (p-31); \draw[line width=2,teal!50] (p-33) -- (p-32); \draw[line width=2,teal!50] (p-34) -- (p-33); \draw[line width=2,teal!50] (p-35) -- (p-33); \draw[line width=2,teal!50] (p-35) -- (p-34); \draw[line width=2,teal!50] (p-36) -- (p-35); \draw[line width=2,teal!50] (p-36) -- (p-34); \draw[line width=2,teal!50] (p-37) -- (p-35); \draw[line width=2,teal!50] (p-37) -- (p-36); \draw[line width=2,teal!50] (p-38) -- (p-37); \draw[line width=2,teal!50] (p-39) -- (p-37); \draw[line width=2,teal!50] (p-39) -- (p-38); \draw[line width=2,teal!50] (p-40) -- (p-39); \draw[line width=2,teal!50] (p-40) -- (p-38); \draw[line width=2,teal!50] (p-41) -- (p-40); \draw[line width=2,teal!50] (p-42) -- (p-41); \draw[line width=2,teal!50] (p-43) -- (p-41); \draw[line width=2,teal!50] (p-43) -- (p-42); \draw[line width=2,teal!50] (p-44) -- (p-43); \draw[line width=2,teal!50] (p-44) -- (p-42); \draw[line width=2,teal!50] (p-45) -- (p-43); \draw[line width=2,teal!50] (p-45) -- (p-44); \draw[line width=2,teal!50] (p-45) -- (p-59); \draw[line width=2,teal!50] (p-46) -- (p-6); \draw[line width=2,teal!50] (p-46) -- (p-3); \draw[line width=2,teal!50] (p-46) -- (p-47); \draw[line width=2,teal!50] (p-47) -- (p-10); \draw[line width=2,teal!50] (p-47) -- (p-8); \draw[line width=2,teal!50] (p-47) -- (p-48); \draw[line width=2,teal!50] (p-48) -- (p-14); \draw[line width=2,teal!50] (p-48) -- (p-12); \draw[line width=2,teal!50] (p-48) -- (p-49); \draw[line width=2,teal!50] (p-49) -- (p-18); \draw[line width=2,teal!50] (p-49) -- (p-16); \draw[line width=2,teal!50] (p-49) -- (p-50); \draw[line width=2,teal!50] (p-50) -- (p-22); \draw[line width=2,teal!50] (p-50) -- (p-20); \draw[line width=2,teal!50] (p-50) -- (p-51); \draw[line width=2,teal!50] (p-51) -- (p-26); \draw[line width=2,teal!50] (p-51) -- (p-24); \draw[line width=2,teal!50] (p-51) -- (p-52); \draw[line width=2,teal!50] (p-52) -- (p-30); \draw[line width=2,teal!50] (p-52) -- (p-28); \draw[line width=2,teal!50] (p-52) -- (p-53); \draw[line width=2,teal!50] (p-53) -- (p-34); \draw[line width=2,teal!50] (p-53) -- (p-32); \draw[line width=2,teal!50] (p-53) -- (p-54); \draw[line width=2,teal!50] (p-54) -- (p-38); \draw[line width=2,teal!50] (p-54) -- (p-36); \draw[line width=2,teal!50] (p-54) -- (p-55); \draw[line width=2,teal!50] (p-55) -- (p-42); \draw[line width=2,teal!50] (p-55) -- (p-40); \draw[line width=2,teal!50] (p-56) -- (p-46); \draw[line width=2,teal!50] (p-56) -- (p-4); \draw[line width=2,teal!50] (p-57) -- (p-56); \draw[line width=2,teal!50] (p-57) -- (p-5); \draw[line width=2,teal!50] (p-59) -- (p-57); \draw[line width=2,teal!50] (p-59) -- (p-60); \draw[line width=2,teal!50] (p-60) -- (p-44); \draw[line width=2,teal!50] (p-60) -- (p-55); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2390, eingetragen 2022-05-08

\quoteon(2022-05-08 09:07 - StefanVogel in Beitrag No. 2388) Ich wills nochmal so formulieren: Bereich 1 ist nicht dadurch bestimmt, dass P55-P60 als Einsetzkante bestimmt wurde, sondern dadurch, dass P55-P60 als Einsetzkante bestimmt wurde \quoteoff Ok, dann müsste man beim 4/10 also doch einfach die zehn am 10er Knoten nacheinander als EK setzen/bestimmen, und bekäme dann jeweils ihren eigenen einfließenden Bereich heraus???


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4173
Wohnort: Raun
  Beitrag No.2391, eingetragen 2022-05-08

\quoteon(2022-05-07 10:54 - haribo in Beitrag No. 2377) button acos1/4 ist bisher noch nicht in meinem verstehen angekommen \quoteoff Das wird extern mit dem GAP-Programm gerechnet. Da kann man mit nicht ineinandergeschachtelten Wurzeln exakt rechnen. Beispiel 60° Winkel \ Ein gleichseitiges Dreieck mit P1=(0,0), P2=(1,0) hat als dritten Eckpunkt P3=(1/2 , 1/2 sqrt(3)) und damit wird die Länge von P1-P3 exakt gleich 1 berechnet. und 30°-Winkel. Innen im Kite befindet sich ein Dreieck mit Seitenlängen 1, 2, 2 und der Basiswinkel berechnet sich aus acos(1/4), daher die Bezeichnung des Buttons. Auch der innere Winkel des Doppelkites #641 lässt sich so berechnen. Das funktioniert aber nicht mit beliebigen Winkeln. [Die Antwort wurde nach Beitrag No.2389 begonnen.]


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4173
Wohnort: Raun
  Beitrag No.2392, eingetragen 2022-05-08

\quoteon(2022-05-08 11:34 - haribo in Beitrag No. 2390) Ok, dann müsste man beim 4/10 also doch einfach die zehn am 10er Knoten nacheinander als EK setzen/bestimmen, und bekäme dann jeweils ihren eigenen einfließenden Bereich heraus??? \quoteoff Man kann die EK nicht beliebig festlegen. Man nimmt eine erste Kante und schaut, ob sich beim Entfernen die Beweglichkeit ändert. Wenn nicht, dann betrachte ich sie als EK und entferne sie. Dann nehme ich irgendeine nächste Kante und probiere, ob sich beim Entfernen der Grad der Beweglichkeit ändert. Wenn nicht, kann ich auch die als EK betrachten und aus dem Graph entfernen. Irgenwann trifft man dann auf eine Kante, wo sich die Beweglichkeit ändert und das ist dann keine EK. Das solange fortsetzen, bis man absolut keine EK mehr findet. Dann hat man alle EK gefunden, also eine von mehreren möglichen Konfigurationen. Man hätte zwischendurch auch andere Kanten versuchen können. Dann nimmt man jede EK einzeln her und setzt sie allein in den Graph ein. Der dann entstehende Spannungsbereich bei geringer Längenänderung ist der zugehörige Bereich. Ich probiere das mal, beim 4/10 nur vom 10er Knoten EK wegnehmen. Ich denke, daß ich nur drei EK schaffe, beim vierten Versuch wird der Graph beweglich. Falls ich es falsch verstanden habe, nochmal \quoteon(2022-05-08 11:34 - haribo in Beitrag No. 2390) Ok, dann müsste man beim 4/10 also doch einfach die zehn am 10er Knoten nacheinander als EK setzen/bestimmen, und bekäme dann jeweils ihren eigenen einfließenden Bereich heraus??? \quoteoff Der Bereich ist nicht durch eine einzelne EK bestimmt. Man muss eine komplette Menge von EK bestimmen. Dann setzt man eine davon ein und die anderen nimmt man heraus. Dafür gibt es dann einen eindeutig bestimmten Bereich. Wenn man noch andere EK drinlässt, erhält man eine Lösungsmenge, weil sich der Bereich der anderen EK mit beliebigen Faktor dazuaddieren kann. Zum Beispiel hellblau+orange. Um das wieder auseinanderzufitzen, müsste man sowieso die anderen EK wieder herausnehmen.


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4173
Wohnort: Raun
  Beitrag No.2393, eingetragen 2022-05-08

Das Ergebnis zum 4/10. Button "acos(1/4)" geht hier nicht, weil die exakten Winkel (zumindestens mir) nicht bekannt sind. Deshalb gerechnet mit Button "GAP", welcher ebenfalls exakt rechnet, aber mit gerundeten Punktkoordinaten. $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/3.74/11.02, 2/3.15/10.21, 3/4.15/10.10, 4/3.55/9.30, 5/2.56/9.41, 6/4.55/9.19, 7/5.33/9.81, 8/5.46/10.80, 9/4.54/10.41, 10/4.67/11.41, 11/5.59/11.79, 12/5.48/8.82, 13/7.37/10.88, 14/6.48/11.34, 15/6.53/10.34, 16/5.64/10.79, 17/5.69/9.79, 18/6.43/9.12, 19/7.43/9.15, 20/6.90/10.00, 21/7.90/10.04, 22/8.43/9.19, 23/4.29/7.20, 24/4.89/8.01, 25/3.89/8.12, 26/4.48/8.93, 27/3.49/9.04, 28/2.70/8.42, 29/2.58/7.42, 30/3.50/7.81, 31/3.37/6.82, 32/2.45/6.43, 33/6.536/7.121, 34/7.43/6.67, 35/7.37/7.67, 36/8.27/7.21, 37/8.32/6.21, 38/8.21/8.21, 39/7.48/8.89, 40/6.48/8.85, 41/7.01/8.00, 42/6.007/7.970, 43/2.98/3.50, 44/6.497/7.098, 45/5.987/7.958, 46/5.50/7.09, 47/4.99/7.95, 48/4.50/7.07, 49/4.76/6.11, 50/5.62/5.60, 51/5.63/6.60, 52/6.49/6.10, 53/6.48/5.10, 54/3.79/6.37, 55/4.95/3.81, 56/5.72/4.46, 57/4.78/4.80, 58/5.55/5.44, 59/4.61/5.78, 60/3.70/5.37, 61/3.34/4.44, 62/4.32/4.59, 63/3.96/3.66, 64/0.81/5.29, 65/0.41/4.37, 66/1.40/4.48, 67/0.99/3.56, 68/0.00/3.46, 69/1.99/3.67, 70/2.62/4.44, 71/2.54/5.44, 72/1.72/4.86, 73/1.63/5.86, 74/5.39/1.12, 75/9.19/4.42, 76/8.76/5.32, 77/8.20/4.49, 78/7.76/5.39, 79/7.20/4.56, 80/7.38/3.57, 81/8.20/3.00, 82/8.29/3.99, 83/9.11/3.42, 84/9.02/2.42, 85/6.44/3.91, 86/7.38/1.27, 87/8.20/1.85, 88/7.29/2.27, 89/8.11/2.84, 90/7.20/3.26, 91/6.26/2.92, 92/5.82/2.02, 93/6.82/2.10, 94/6.39/1.20, 95/3.70/0.05, 96/4.55/0.59, 97/3.66/1.05, 98/4.50/1.59, 99/3.62/2.05, 100/2.66/1.76, 101/2.18/0.88, 102/3.18/0.90, 103/2.70/0.02, 104/1.70/0.00, 105/2.89/2.73, 106/0.37/1.49, 107/1.04/0.75, 108/1.35/1.70, 109/2.02/0.95, 110/2.33/1.90, 111/1.89/2.80, 112/0.94/3.13, 113/1.13/2.14, 114/0.19/2.47} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-1) -- (p-9); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-1) -- (p-9); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-1) -- (p-9); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-1) -- (p-10); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-1) -- (p-10); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-2) -- (p-1); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-2) -- (p-1); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-2) -- (p-1); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-3) -- (p-1); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-3) -- (p-1); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-3) -- (p-1); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-3) -- (p-2); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-3) -- (p-2); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-3) -- (p-2); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-4) -- (p-3); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-4) -- (p-3); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-4) -- (p-3); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-4) -- (p-2); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-4) -- (p-2); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-4) -- (p-2); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-5) -- (p-4); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-5) -- (p-2); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-5) -- (p-27); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-5) -- (p-28); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-6) -- (p-3); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-6) -- (p-3); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-6) -- (p-3); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-6) -- (p-4); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-6) -- (p-4); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-6) -- (p-4); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-6) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-6) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-6) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-8) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-8) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-9) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-9) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-9) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-11) -- (p-8); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-11) -- (p-8); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-11) -- (p-10); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-11) -- (p-10); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-11) -- (p-14); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-11) -- (p-14); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-11) -- (p-16); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-11) -- (p-16); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-12) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-12) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-12) -- (p-7); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-12) -- (p-6); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-12) -- (p-6); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-12) -- (p-6); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-12) -- (p-17); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-12) -- (p-17); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-12) -- (p-18); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-12) -- (p-18); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-12) -- (p-24); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 5.33pt,red!50] (p-12) -- (p-26); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-12) -- (p-40); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-12) -- (p-42); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-13) -- (p-20); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-13) -- (p-20); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-13) -- (p-21); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-13) -- (p-21); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-14) -- (p-13); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-14) -- (p-13); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 1.33pt,orange!50] (p-15) -- (p-13); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 2.67pt,green!50] (p-15) -- (p-13); 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\draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-103) -- (p-101); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-103) -- (p-102); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-104) -- (p-101); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-104) -- (p-103); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-104) -- (p-107); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-104) -- (p-109); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-105) -- (p-99); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-105) -- (p-100); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-105) -- (p-110); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-105) -- (p-111); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-106) -- (p-113); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-106) -- (p-114); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-107) -- (p-106); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-108) -- (p-106); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-108) -- (p-107); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-109) -- (p-107); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-109) -- (p-108); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-110) -- (p-108); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-110) -- (p-109); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-110) -- (p-111); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-112) -- (p-111); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-113) -- (p-111); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-113) -- (p-112); \draw[line width=2,dash=on 1.33pt off 6.67pt phase 6.67pt,violet!50] (p-114) -- (p-112); \draw[line width=2,violet!50] (p-114) -- (p-113); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 1/9, 1/10, 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 5/27, 5/28, 6/3, 6/4, 6/7, 8/7, 9/7, 9/8, 10/8, 10/9, 11/8, 11/10, 11/14, 11/16, 12/7, 12/6, 12/17, 12/18, 12/24, 12/26, 12/40, 12/42, 12/45, 12/47, 13/20, 13/21, 14/13, 15/13, 15/14, 16/14, 16/15, 17/15, 17/16, 17/18, 19/18, 20/18, 20/19, 21/19, 21/20, 22/19, 22/21, 22/38, 22/39, 23/30, 23/31, 24/23, 25/23, 25/24, 26/24, 26/25, 27/25, 27/26, 27/28, 29/28, 30/28, 30/29, 31/29, 31/30, 32/29, 32/31, 32/71, 32/73, 33/41, 33/42, 34/33, 35/33, 35/34, 36/34, 36/35, 37/34, 37/36, 37/76, 37/78, 38/35, 38/36, 38/39, 40/39, 41/39, 41/40, 42/40, 42/41, 43/61, 43/63, 43/69, 43/70, 44/51, 44/52, 45/44, 46/44, 46/45, 47/45, 47/46, 48/46, 48/47, 48/49, 50/49, 51/49, 51/50, 52/50, 52/51, 53/50, 53/52, 53/56, 53/58, 54/48, 54/49, 54/59, 54/60, 55/62, 55/63, 56/55, 57/55, 57/56, 58/56, 58/57, 59/57, 59/58, 59/60, 61/60, 62/60, 62/61, 63/61, 63/62, 64/72, 64/73, 65/64, 66/64, 66/65, 67/65, 67/66, 68/65, 68/67, 68/112, 68/114, 69/66, 69/67, 69/70, 71/70, 72/70, 72/71, 73/71, 73/72, 74/92, 74/94, 74/96, 74/98, 75/82, 75/83, 76/75, 77/75, 77/76, 78/76, 78/77, 79/77, 79/78, 79/80, 81/80, 82/80, 82/81, 83/81, 83/82, 84/81, 84/83, 84/87, 84/89, 85/79, 85/80, 85/90, 85/91, 86/93, 86/94, 87/86, 88/86, 88/87, 89/87, 89/88, 90/88, 90/89, 90/91, 92/91, 93/91, 93/92, 94/92, 94/93, 95/102, 95/103, 96/95, 97/95, 97/96, 98/96, 98/97, 99/97, 99/98, 99/100, 101/100, 102/100, 102/101, 103/101, 103/102, 104/101, 104/103, 104/107, 104/109, 105/99, 105/100, 105/110, 105/111, 106/113, 106/114, 107/106, 108/106, 108/107, 109/107, 109/108, 110/108, 110/109, 110/111, 112/111, 113/111, 113/112, 114/112, 114/113} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/84, 2/144, 3/24, 4/324, 5/128, 6/324, 7/68, 8/293, 9/173, 10/53, 11/123, 12/24, 13/3, 14/123, 15/303, 16/123, 17/243, 18/348, 19/332, 20/92, 21/92, 22/48, 23/264, 24/324, 25/204, 26/24, 27/144, 28/113, 29/113, 30/53, 31/233, 32/233, 33/183, 34/183, 35/63, 36/303, 37/86, 38/63, 39/168, 40/92, 41/272, 42/152, 43/321, 44/331, 45/331, 46/211, 47/151, 48/75, 49/180, 50/180, 51/120, 52/360, 53/300, 54/195, 55/339, 56/10, 57/250, 58/70, 59/354, 60/234, 61/99, 62/339, 63/219, 64/96, 65/96, 66/336, 67/216, 68/216, 69/336, 70/81, 71/305, 72/185, 73/65, 74/2, 75/326, 76/326, 77/326, 78/146, 79/70, 80/310, 81/175, 82/175, 83/355, 84/5, 85/190, 86/245, 87/5, 88/245, 89/125, 90/350, 91/230, 92/94, 93/334, 94/334, 95/242, 96/302, 97/182, 98/122, 99/122, 100/91, 101/91, 102/331, 103/331, 104/282, 105/107, 106/162, 107/222, 108/42, 109/42, 110/266, 111/146, 112/11, 113/251, 114/251} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Button "GAP" hat als Einsetzkanten P60-P62 hellgrau mitte P28-P30 rot mitte links P20-P21 grün oben P41-P42 orange mitte rechts P93-P94 hellblau unten rechts P113-P114 violet unten links gewählt. Diese Einsetzkanten sind im Graph als durchgehende Linien gezeichnet, die dazugehörigen Bereiche als gepunktete Linie. Wegen der gerundeten Eingangsdaten sind die Bereiche etwas gröẞer als bei exakten Eingangsdaten, wie im gestrichelten Graph #2366-3 schonmal gezeichnet. Nur der orange Bereich rechts oben läuft sehr weit nach links in den grünen Bereich mit hinein. Da muss ich nochmal schauen, ob das noch andere Ursachen hat als nur die gerundeten Punktkoordinaten.


   Profil
StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4173
Wohnort: Raun
  Beitrag No.2394, eingetragen 2022-05-08

\quoteon(2022-05-07 10:49 - haribo in Beitrag No. 2376) also glaubst du der 120er hat einfach 4EK? passt dass zu den auf den 120er basierenden 4/5 [erfordert 4EK]; 4/6 [4EK]; 4/7[6EK]; 4/8 [6EK] ? [#2350; #2351, #2352] haben die also ihre teilweise, also jedenfals der 4/7 und 4/8er, zusätzlich erforderlichen zwei EK´s dann alle im mittelraum ? ich frag weil kites im mittelraum gibt es ja keine, dann muss es dort andere EK-generierende konstrukte geben, und die wären ja mal interessant herauszuarbeiten, insbesondere weil die ja evtl kleiner als kites sind? Nachtrag: könnte auch sein dass die innenkonstrukte im zusammenhang mit den äusseren wirken beim generieren von EK´s, dann sind sie möglöicherweise grösser als kites??? \quoteoff #2350 #2351 #2352 habe ich geringfügig so verstellt, dass Winkel ∠(P2,P1,P6) nahe 90° ist. Dann geht Button "acos(1/4)" exakt Rechnen mit exakten Punktkoordinaten. Ich erhalte immer Bereiche, die nahezu den gesamten Graph umfassen. Irgendein wiederkehrender kleiner Teilgraph ist nicht erkennbar. #2350 $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/2.87/3.23, 62/2.87/4.23, 63/3.73/3.73, 64/3.73/2.73, 65/4.60/3.23, 66/4.60/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-2) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-2); \draw[line width=2,blue!50] (p-4) -- (p-3); \draw[line width=2,blue!50] (p-4) -- (p-2); \draw[line width=2,blue!50] (p-5) -- (p-4); \draw[line width=2,blue!50] (p-5) -- (p-2); \draw[line width=2,blue!50] (p-6) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-6); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-6); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-8); \draw[line width=2,blue!50] (p-10) -- (p-9); \draw[line width=2,blue!50] (p-10) -- (p-51); \draw[line width=2,blue!50] (p-11) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-12) -- (p-11); \draw[line width=2,blue!50] (p-12) -- (p-10); \draw[line width=2,blue!50] (p-13) -- (p-11); \draw[line width=2,blue!50] (p-13) -- (p-12); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-14) -- (p-52); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-16) -- (p-14); \draw[line width=2,blue!50] (p-16) -- (p-53); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-18) -- (p-17); \draw[line width=2,blue!50] (p-18) -- (p-53); \draw[line width=2,blue!50] (p-19) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-19); \draw[line width=2,blue!50] (p-20) -- (p-18); \draw[line width=2,blue!50] (p-21) -- (p-19); \draw[line width=2,blue!50] (p-21) -- (p-20); \draw[line width=2,blue!50] (p-22) -- (p-21); \draw[line width=2,blue!50] (p-22) -- (p-54); \draw[line width=2,blue!50] (p-23) -- (p-21); \draw[line width=2,blue!50] (p-23) -- (p-22); \draw[line width=2,blue!50] (p-24) -- (p-23); \draw[line width=2,blue!50] (p-24) -- (p-22); \draw[line width=2,blue!50] (p-25) -- (p-23); \draw[line width=2,blue!50] (p-25) -- (p-24); \draw[line width=2,blue!50] (p-26) -- (p-55); \draw[line width=2,blue!50] (p-27) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-26); \draw[line width=2,blue!50] (p-28) -- (p-29); \draw[line width=2,blue!50] (p-28) -- (p-55); \draw[line width=2,blue!50] (p-29) -- (p-27); \draw[line width=2,blue!50] (p-29) -- (p-26); \draw[line width=2,blue!50] (p-30) -- (p-27); \draw[line width=2,blue!50] (p-30) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-30); \draw[line width=2,blue!50] (p-31) -- (p-28); \draw[line width=2,blue!50] (p-32) -- (p-30); \draw[line width=2,blue!50] (p-32) -- (p-31); \draw[line width=2,blue!50] (p-33) -- (p-32); \draw[line width=2,blue!50] (p-33) -- (p-31); \draw[line width=2,blue!50] (p-34) -- (p-32); \draw[line width=2,blue!50] (p-34) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-34); \draw[line width=2,blue!50] (p-36) -- (p-34); \draw[line width=2,blue!50] (p-36) -- (p-35); \draw[line width=2,blue!50] (p-37) -- (p-36); \draw[line width=2,blue!50] (p-37) -- (p-35); \draw[line width=2,blue!50] (p-38) -- (p-37); \draw[line width=2,blue!50] (p-39) -- (p-38); \draw[line width=2,blue!50] (p-39) -- (p-57); \draw[line width=2,blue!50] (p-40) -- (p-38); \draw[line width=2,blue!50] (p-41) -- (p-39); \draw[line width=2,blue!50] (p-42) -- (p-40); \draw[line width=2,blue!50] (p-42) -- (p-41); \draw[line width=2,blue!50] (p-43) -- (p-42); \draw[line width=2,blue!50] (p-43) -- (p-58); \draw[line width=2,blue!50] (p-44) -- (p-43); \draw[line width=2,blue!50] (p-44) -- (p-46); \draw[line width=2,blue!50] (p-45) -- (p-44); \draw[line width=2,blue!50] (p-45) -- (p-43); \draw[line width=2,blue!50] (p-45) -- (p-46); \draw[line width=2,blue!50] (p-46) -- (p-47); \draw[line width=2,blue!50] (p-46) -- (p-48); \draw[line width=2,blue!50] (p-47) -- (p-49); \draw[line width=2,blue!50] (p-47) -- (p-48); \draw[line width=2,blue!50] (p-48) -- (p-49); \draw[line width=2,blue!50] (p-48) -- (p-5); \draw[line width=2,blue!50] (p-49) -- (p-60); \draw[line width=2,blue!50] (p-49) -- (p-5); \draw[line width=2,blue!50] (p-50) -- (p-3); \draw[line width=2,blue!50] (p-50) -- (p-60); \draw[line width=2,blue!50] (p-51) -- (p-8); \draw[line width=2,blue!50] (p-51) -- (p-50); \draw[line width=2,blue!50] (p-52) -- (p-12); \draw[line width=2,blue!50] (p-52) -- (p-61); \draw[line width=2,blue!50] (p-53) -- (p-52); \draw[line width=2,blue!50] (p-53) -- (p-62); \draw[line width=2,blue!50] (p-54) -- (p-20); \draw[line width=2,blue!50] (p-54) -- (p-62); \draw[line width=2,blue!50] (p-55) -- (p-54); \draw[line width=2,blue!50] (p-57) -- (p-37); \draw[line width=2,blue!50] (p-58) -- (p-41); \draw[line width=2,blue!50] (p-58) -- (p-57); \draw[line width=2,blue!50] (p-60) -- (p-4); \draw[line width=2,blue!50] (p-61) -- (p-51); \draw[line width=2,blue!50] (p-62) -- (p-61); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/50, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 10/51, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 14/52, 15/13, 15/14, 16/15, 16/14, 16/53, 17/15, 17/16, 18/17, 18/53, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 22/54, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 26/55, 27/25, 27/26, 28/29, 28/55, 29/27, 29/26, 30/27, 30/29, 31/30, 31/28, 32/30, 32/31, 33/32, 33/31, 34/32, 34/33, 35/34, 35/56, 36/34, 36/35, 37/36, 37/35, 38/36, 38/37, 39/38, 39/57, 40/38, 40/39, 41/40, 41/39, 42/40, 42/41, 43/42, 43/58, 44/42, 44/43, 44/46, 45/44, 45/43, 45/59, 45/46, 46/47, 46/48, 47/49, 47/48, 48/49, 48/5, 49/60, 49/5, 50/3, 50/60, 51/8, 51/50, 52/12, 52/61, 53/52, 53/62, 54/20, 54/62, 55/24, 55/54, 56/33, 56/28, 56/66, 57/37, 57/66, 58/41, 58/57, 59/47, 59/58, 59/65, 60/4, 61/51, 61/63, 62/61, 62/63, 63/64, 63/65, 64/50, 64/60, 65/64, 66/63, 66/65} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/90, 4/30, 5/330, 6/360, 7/180, 8/120, 9/180, 10/30, 11/270, 12/30, 13/150, 14/360, 15/120, 16/360, 17/210, 18/330, 19/210, 20/30, 21/180, 22/240, 23/180, 24/300, 25/150, 26/210, 27/30, 28/198, 29/270, 30/30, 31/180, 32/360, 33/240, 34/90, 35/210, 36/30, 37/270, 38/330, 39/120, 40/360, 41/180, 42/300, 43/150, 44/270, 45/210, 46/270, 47/120, 48/360, 49/180, 50/210, 51/198, 52/318, 53/138, 54/258, 55/348, 56/18, 57/138, 58/108, 59/273, 60/330, 61/240, 62/120, 63/120, 64/90, 65/360, 66/60} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/2.87/3.23, 62/2.87/4.23, 63/3.73/3.73, 64/3.73/2.73, 65/4.60/3.23, 66/4.60/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,orange!50] (p-2) -- (p-1); \draw[line width=2,orange!50] (p-3) -- (p-1); \draw[line width=2,orange!50] (p-3) -- (p-2); \draw[line width=2,orange!50] (p-4) -- (p-3); \draw[line width=2,orange!50] (p-4) -- (p-2); \draw[line width=2,orange!50] (p-5) -- (p-4); \draw[line width=2,orange!50] (p-5) -- (p-2); \draw[line width=2,orange!50] (p-6) -- (p-1); \draw[line width=2,orange!50] (p-6) -- (p-50); \draw[line width=2,orange!50] (p-7) -- (p-1); \draw[line width=2,orange!50] (p-7) -- (p-6); \draw[line width=2,orange!50] (p-8) -- (p-7); \draw[line width=2,orange!50] (p-8) -- (p-6); \draw[line width=2,orange!50] (p-9) -- (p-7); \draw[line width=2,orange!50] (p-9) -- (p-8); \draw[line width=2,orange!50] (p-10) -- (p-9); \draw[line width=2,orange!50] (p-10) -- (p-51); \draw[line width=2,orange!50] (p-11) -- (p-9); \draw[line width=2,orange!50] (p-11) -- (p-10); \draw[line width=2,orange!50] (p-12) -- (p-11); \draw[line width=2,orange!50] (p-12) -- (p-10); \draw[line width=2,orange!50] (p-13) -- (p-11); \draw[line width=2,orange!50] (p-13) -- (p-12); \draw[line width=2,orange!50] (p-14) -- (p-13); \draw[line width=2,orange!50] (p-14) -- (p-52); \draw[line width=2,orange!50] (p-15) -- (p-13); \draw[line width=2,orange!50] (p-15) -- (p-14); \draw[line width=2,orange!50] (p-16) -- (p-15); \draw[line width=2,orange!50] (p-16) -- (p-14); \draw[line width=2,orange!50] (p-16) -- (p-53); \draw[line width=2,orange!50] (p-17) -- (p-15); \draw[line width=2,orange!50] (p-17) -- (p-16); \draw[line width=2,orange!50] (p-18) -- (p-17); \draw[line width=2,orange!50] (p-18) -- (p-53); \draw[line width=2,orange!50] (p-19) -- (p-17); \draw[line width=2,orange!50] (p-19) -- (p-18); \draw[line width=2,orange!50] (p-20) -- (p-19); \draw[line width=2,orange!50] (p-20) -- (p-18); \draw[line width=2,orange!50] (p-21) -- (p-19); \draw[line width=2,orange!50] (p-21) -- (p-20); \draw[line width=2,orange!50] (p-22) -- (p-21); \draw[line width=2,orange!50] (p-22) -- (p-54); \draw[line width=2,orange!50] (p-23) -- (p-21); \draw[line width=2,orange!50] (p-23) -- (p-22); \draw[line width=2,orange!50] (p-24) -- (p-23); \draw[line width=2,orange!50] (p-24) -- (p-22); \draw[line width=2,orange!50] (p-25) -- (p-23); \draw[line width=2,orange!50] (p-25) -- (p-24); \draw[line width=2,orange!50] (p-26) -- (p-25); \draw[line width=2,orange!50] (p-26) -- (p-55); \draw[line width=2,orange!50] (p-27) -- (p-25); \draw[line width=2,orange!50] (p-27) -- (p-26); \draw[line width=2,orange!50] (p-28) -- (p-29); \draw[line width=2,orange!50] (p-28) -- (p-55); \draw[line width=2,orange!50] (p-29) -- (p-27); \draw[line width=2,orange!50] (p-29) -- (p-26); \draw[line width=2,orange!50] (p-30) -- (p-27); \draw[line width=2,orange!50] (p-30) -- (p-29); \draw[line width=2,orange!50] (p-31) -- (p-30); \draw[line width=2,orange!50] (p-31) -- (p-28); \draw[line width=2,orange!50] (p-32) -- (p-30); \draw[line width=2,orange!50] (p-32) -- (p-31); \draw[line width=2,orange!50] (p-33) -- (p-32); \draw[line width=2,orange!50] (p-33) -- (p-31); \draw[line width=2,orange!50] (p-34) -- (p-32); \draw[line width=2,orange!50] (p-34) -- (p-33); \draw[line width=2,orange!50] (p-35) -- (p-34); \draw[line width=2,orange!50] (p-35) -- (p-56); \draw[line width=2,orange!50] (p-36) -- (p-34); \draw[line width=2,orange!50] (p-36) -- (p-35); \draw[line width=2,orange!50] (p-37) -- (p-36); \draw[line width=2,orange!50] (p-37) -- (p-35); \draw[line width=2,orange!50] (p-38) -- (p-36); \draw[line width=2,orange!50] (p-38) -- (p-37); \draw[line width=2,orange!50] (p-39) -- (p-38); \draw[line width=2,orange!50] (p-39) -- (p-57); \draw[line width=2,orange!50] (p-40) -- (p-38); \draw[line width=2,orange!50] (p-40) -- (p-39); \draw[line width=2,orange!50] (p-41) -- (p-40); \draw[line width=2,orange!50] (p-41) -- (p-39); \draw[line width=2,orange!50] (p-42) -- (p-40); \draw[line width=2,orange!50] (p-42) -- (p-41); \draw[line width=2,orange!50] (p-43) -- (p-42); \draw[line width=2,orange!50] (p-43) -- (p-58); \draw[line width=2,orange!50] (p-44) -- (p-42); \draw[line width=2,orange!50] (p-44) -- (p-43); \draw[line width=2,orange!50] (p-44) -- (p-46); \draw[line width=2,orange!50] (p-45) -- (p-44); \draw[line width=2,orange!50] (p-45) -- (p-43); \draw[line width=2,orange!50] (p-45) -- (p-59); \draw[line width=2,orange!50] (p-45) -- (p-46); \draw[line width=2,orange!50] (p-46) -- (p-47); \draw[line width=2,orange!50] (p-46) -- (p-48); \draw[line width=2,orange!50] (p-47) -- (p-49); \draw[line width=2,orange!50] (p-47) -- (p-48); \draw[line width=2,orange!50] (p-48) -- (p-49); \draw[line width=2,orange!50] (p-48) -- (p-5); \draw[line width=2,orange!50] (p-49) -- (p-60); \draw[line width=2,orange!50] (p-49) -- (p-5); \draw[line width=2,orange!50] (p-50) -- (p-3); \draw[line width=2,orange!50] (p-50) -- (p-60); \draw[line width=2,orange!50] (p-51) -- (p-8); \draw[line width=2,orange!50] (p-51) -- (p-50); \draw[line width=2,orange!50] (p-52) -- (p-12); \draw[line width=2,orange!50] (p-52) -- (p-61); \draw[line width=2,orange!50] (p-53) -- (p-52); \draw[line width=2,orange!50] (p-53) -- (p-62); \draw[line width=2,orange!50] (p-54) -- (p-20); \draw[line width=2,orange!50] (p-54) -- (p-62); \draw[line width=2,orange!50] (p-55) -- (p-24); \draw[line width=2,orange!50] (p-55) -- (p-54); \draw[line width=2,orange!50] (p-56) -- (p-33); \draw[line width=2,orange!50] (p-56) -- (p-28); \draw[line width=2,orange!50] (p-57) -- (p-37); \draw[line width=2,orange!50] (p-58) -- (p-41); \draw[line width=2,orange!50] (p-58) -- (p-57); \draw[line width=2,orange!50] (p-59) -- (p-47); \draw[line width=2,orange!50] (p-59) -- (p-58); \draw[line width=2,orange!50] (p-60) -- (p-4); \draw[line width=2,orange!50] (p-61) -- (p-51); \draw[line width=2,orange!50] (p-61) -- (p-63); \draw[line width=2,orange!50] (p-62) -- (p-63); \draw[line width=2,orange!50] (p-63) -- (p-64); \draw[line width=2,orange!50] (p-64) -- (p-50); \draw[line width=2,orange!50] (p-64) -- (p-60); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/2.87/3.23, 62/2.87/4.23, 63/3.73/3.73, 64/3.73/2.73, 65/4.60/3.23, 66/4.60/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,green!50] (p-2) -- (p-1); \draw[line width=2,green!50] (p-3) -- (p-1); \draw[line width=2,green!50] (p-3) -- (p-2); \draw[line width=2,green!50] (p-4) -- (p-3); \draw[line width=2,green!50] (p-4) -- (p-2); \draw[line width=2,green!50] (p-5) -- (p-4); \draw[line width=2,green!50] (p-5) -- (p-2); \draw[line width=2,green!50] (p-6) -- (p-1); \draw[line width=2,green!50] (p-6) -- (p-50); \draw[line width=2,green!50] (p-7) -- (p-1); \draw[line width=2,green!50] (p-7) -- (p-6); \draw[line width=2,green!50] (p-8) -- (p-7); \draw[line width=2,green!50] (p-8) -- (p-6); \draw[line width=2,green!50] (p-9) -- (p-7); \draw[line width=2,green!50] (p-9) -- (p-8); \draw[line width=2,green!50] (p-10) -- (p-9); \draw[line width=2,green!50] (p-10) -- (p-51); \draw[line width=2,green!50] (p-11) -- (p-9); \draw[line width=2,green!50] (p-11) -- (p-10); \draw[line width=2,green!50] (p-12) -- (p-11); \draw[line width=2,green!50] (p-12) -- (p-10); \draw[line width=2,green!50] (p-13) -- (p-11); \draw[line width=2,green!50] (p-13) -- (p-12); \draw[line width=2,green!50] (p-14) -- (p-13); \draw[line width=2,green!50] (p-14) -- (p-52); \draw[line width=2,green!50] (p-15) -- (p-13); \draw[line width=2,green!50] (p-16) -- (p-14); \draw[line width=2,green!50] (p-16) -- (p-53); \draw[line width=2,green!50] (p-17) -- (p-15); \draw[line width=2,green!50] (p-17) -- (p-16); \draw[line width=2,green!50] (p-18) -- (p-17); \draw[line width=2,green!50] (p-18) -- (p-53); \draw[line width=2,green!50] (p-19) -- (p-17); \draw[line width=2,green!50] (p-19) -- (p-18); \draw[line width=2,green!50] (p-20) -- (p-19); \draw[line width=2,green!50] (p-20) -- (p-18); \draw[line width=2,green!50] (p-21) -- (p-19); \draw[line width=2,green!50] (p-21) -- (p-20); \draw[line width=2,green!50] (p-22) -- (p-21); \draw[line width=2,green!50] (p-22) -- (p-54); \draw[line width=2,green!50] (p-23) -- (p-21); \draw[line width=2,green!50] (p-23) -- (p-22); \draw[line width=2,green!50] (p-24) -- (p-23); \draw[line width=2,green!50] (p-24) -- (p-22); \draw[line width=2,green!50] (p-25) -- (p-23); \draw[line width=2,green!50] (p-25) -- (p-24); \draw[line width=2,green!50] (p-26) -- (p-25); \draw[line width=2,green!50] (p-26) -- (p-55); \draw[line width=2,green!50] (p-27) -- (p-25); \draw[line width=2,green!50] (p-27) -- (p-26); \draw[line width=2,green!50] (p-28) -- (p-29); \draw[line width=2,green!50] (p-28) -- (p-55); \draw[line width=2,green!50] (p-29) -- (p-27); \draw[line width=2,green!50] (p-29) -- (p-26); \draw[line width=2,green!50] (p-30) -- (p-27); \draw[line width=2,green!50] (p-30) -- (p-29); \draw[line width=2,green!50] (p-31) -- (p-30); \draw[line width=2,green!50] (p-31) -- (p-28); \draw[line width=2,green!50] (p-32) -- (p-30); \draw[line width=2,green!50] (p-32) -- (p-31); \draw[line width=2,green!50] (p-33) -- (p-32); \draw[line width=2,green!50] (p-33) -- (p-31); \draw[line width=2,green!50] (p-34) -- (p-32); \draw[line width=2,green!50] (p-34) -- (p-33); \draw[line width=2,green!50] (p-35) -- (p-34); \draw[line width=2,green!50] (p-35) -- (p-56); \draw[line width=2,green!50] (p-36) -- (p-34); \draw[line width=2,green!50] (p-36) -- (p-35); \draw[line width=2,green!50] (p-37) -- (p-36); \draw[line width=2,green!50] (p-37) -- (p-35); \draw[line width=2,green!50] (p-38) -- (p-36); \draw[line width=2,green!50] (p-38) -- (p-37); \draw[line width=2,green!50] (p-39) -- (p-38); \draw[line width=2,green!50] (p-39) -- (p-57); \draw[line width=2,green!50] (p-40) -- (p-38); \draw[line width=2,green!50] (p-40) -- (p-39); \draw[line width=2,green!50] (p-41) -- (p-40); \draw[line width=2,green!50] (p-41) -- (p-39); \draw[line width=2,green!50] (p-42) -- (p-40); \draw[line width=2,green!50] (p-42) -- (p-41); \draw[line width=2,green!50] (p-43) -- (p-42); \draw[line width=2,green!50] (p-43) -- (p-58); \draw[line width=2,green!50] (p-44) -- (p-42); \draw[line width=2,green!50] (p-44) -- (p-43); \draw[line width=2,green!50] (p-44) -- (p-46); \draw[line width=2,green!50] (p-45) -- (p-44); \draw[line width=2,green!50] (p-45) -- (p-43); \draw[line width=2,green!50] (p-45) -- (p-59); \draw[line width=2,green!50] (p-45) -- (p-46); \draw[line width=2,green!50] (p-46) -- (p-47); \draw[line width=2,green!50] (p-46) -- (p-48); \draw[line width=2,green!50] (p-47) -- (p-49); \draw[line width=2,green!50] (p-47) -- (p-48); \draw[line width=2,green!50] (p-48) -- (p-49); \draw[line width=2,green!50] (p-48) -- (p-5); \draw[line width=2,green!50] (p-49) -- (p-60); \draw[line width=2,green!50] (p-49) -- (p-5); \draw[line width=2,green!50] (p-50) -- (p-3); \draw[line width=2,green!50] (p-50) -- (p-60); \draw[line width=2,green!50] (p-51) -- (p-8); \draw[line width=2,green!50] (p-51) -- (p-50); \draw[line width=2,green!50] (p-52) -- (p-12); \draw[line width=2,green!50] (p-52) -- (p-61); \draw[line width=2,green!50] (p-53) -- (p-52); \draw[line width=2,green!50] (p-53) -- (p-62); \draw[line width=2,green!50] (p-54) -- (p-20); \draw[line width=2,green!50] (p-54) -- (p-62); \draw[line width=2,green!50] (p-55) -- (p-24); \draw[line width=2,green!50] (p-55) -- (p-54); \draw[line width=2,green!50] (p-56) -- (p-33); \draw[line width=2,green!50] (p-56) -- (p-28); \draw[line width=2,green!50] (p-57) -- (p-37); \draw[line width=2,green!50] (p-58) -- (p-41); \draw[line width=2,green!50] (p-58) -- (p-57); \draw[line width=2,green!50] (p-59) -- (p-47); \draw[line width=2,green!50] (p-59) -- (p-58); \draw[line width=2,green!50] (p-59) -- (p-65); \draw[line width=2,green!50] (p-60) -- (p-4); \draw[line width=2,green!50] (p-61) -- (p-51); \draw[line width=2,green!50] (p-61) -- (p-63); \draw[line width=2,green!50] (p-62) -- (p-63); \draw[line width=2,green!50] (p-63) -- (p-64); \draw[line width=2,green!50] (p-63) -- (p-65); \draw[line width=2,green!50] (p-64) -- (p-50); \draw[line width=2,green!50] (p-65) -- (p-64); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/2.87/3.23, 62/2.87/4.23, 63/3.73/3.73, 64/3.73/2.73, 65/4.60/3.23, 66/4.60/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,darkgray!50] (p-2) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-2); \draw[line width=2,darkgray!50] (p-4) -- (p-3); \draw[line width=2,darkgray!50] (p-4) -- (p-2); \draw[line width=2,darkgray!50] (p-5) -- (p-4); \draw[line width=2,darkgray!50] (p-5) -- (p-2); \draw[line width=2,darkgray!50] (p-6) -- (p-1); \draw[line width=2,darkgray!50] (p-6) -- (p-50); \draw[line width=2,darkgray!50] (p-7) -- (p-1); \draw[line width=2,darkgray!50] (p-7) -- (p-6); \draw[line width=2,darkgray!50] (p-8) -- (p-7); \draw[line width=2,darkgray!50] (p-8) -- (p-6); \draw[line width=2,darkgray!50] (p-9) -- (p-7); \draw[line width=2,darkgray!50] (p-9) -- (p-8); \draw[line width=2,darkgray!50] (p-10) -- (p-9); \draw[line width=2,darkgray!50] (p-10) -- (p-51); \draw[line width=2,darkgray!50] (p-11) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-10); \draw[line width=2,darkgray!50] (p-12) -- (p-11); \draw[line width=2,darkgray!50] (p-12) -- (p-10); \draw[line width=2,darkgray!50] (p-13) -- (p-11); \draw[line width=2,darkgray!50] (p-13) -- (p-12); \draw[line width=2,darkgray!50] (p-14) -- (p-13); \draw[line width=2,darkgray!50] (p-14) -- (p-52); \draw[line width=2,darkgray!50] (p-15) -- (p-13); \draw[line width=2,darkgray!50] (p-15) -- (p-14); \draw[line width=2,darkgray!50] (p-16) -- (p-15); \draw[line width=2,darkgray!50] (p-16) -- (p-14); \draw[line width=2,darkgray!50] (p-16) -- (p-53); \draw[line width=2,darkgray!50] (p-17) -- (p-15); \draw[line width=2,darkgray!50] (p-17) -- (p-16); \draw[line width=2,darkgray!50] (p-18) -- (p-17); \draw[line width=2,darkgray!50] (p-18) -- (p-53); \draw[line width=2,darkgray!50] (p-19) -- (p-17); \draw[line width=2,darkgray!50] (p-19) -- (p-18); \draw[line width=2,darkgray!50] (p-20) -- (p-19); \draw[line width=2,darkgray!50] (p-20) -- (p-18); \draw[line width=2,darkgray!50] (p-21) -- (p-19); \draw[line width=2,darkgray!50] (p-21) -- (p-20); \draw[line width=2,darkgray!50] (p-22) -- (p-21); \draw[line width=2,darkgray!50] (p-22) -- (p-54); \draw[line width=2,darkgray!50] (p-23) -- (p-21); \draw[line width=2,darkgray!50] (p-24) -- (p-22); \draw[line width=2,darkgray!50] (p-25) -- (p-23); \draw[line width=2,darkgray!50] (p-25) -- (p-24); \draw[line width=2,darkgray!50] (p-26) -- (p-25); \draw[line width=2,darkgray!50] (p-26) -- (p-55); \draw[line width=2,darkgray!50] (p-27) -- (p-25); \draw[line width=2,darkgray!50] (p-27) -- (p-26); \draw[line width=2,darkgray!50] (p-28) -- (p-29); \draw[line width=2,darkgray!50] (p-29) -- (p-27); \draw[line width=2,darkgray!50] (p-29) -- (p-26); \draw[line width=2,darkgray!50] (p-30) -- (p-27); \draw[line width=2,darkgray!50] (p-30) -- (p-29); \draw[line width=2,darkgray!50] (p-31) -- (p-30); \draw[line width=2,darkgray!50] (p-31) -- (p-28); \draw[line width=2,darkgray!50] (p-32) -- (p-30); \draw[line width=2,darkgray!50] (p-32) -- (p-31); \draw[line width=2,darkgray!50] (p-33) -- (p-32); \draw[line width=2,darkgray!50] (p-33) -- (p-31); \draw[line width=2,darkgray!50] (p-34) -- (p-32); \draw[line width=2,darkgray!50] (p-34) -- (p-33); \draw[line width=2,darkgray!50] (p-35) -- (p-34); \draw[line width=2,darkgray!50] (p-35) -- (p-56); \draw[line width=2,darkgray!50] (p-36) -- (p-34); \draw[line width=2,darkgray!50] (p-36) -- (p-35); \draw[line width=2,darkgray!50] (p-37) -- (p-36); \draw[line width=2,darkgray!50] (p-37) -- (p-35); \draw[line width=2,darkgray!50] (p-38) -- (p-36); \draw[line width=2,darkgray!50] (p-38) -- (p-37); \draw[line width=2,darkgray!50] (p-39) -- (p-38); \draw[line width=2,darkgray!50] (p-39) -- (p-57); \draw[line width=2,darkgray!50] (p-40) -- (p-38); \draw[line width=2,darkgray!50] (p-40) -- (p-39); \draw[line width=2,darkgray!50] (p-41) -- (p-40); \draw[line width=2,darkgray!50] (p-41) -- (p-39); \draw[line width=2,darkgray!50] (p-42) -- (p-40); \draw[line width=2,darkgray!50] (p-42) -- (p-41); \draw[line width=2,darkgray!50] (p-43) -- (p-42); \draw[line width=2,darkgray!50] (p-43) -- (p-58); \draw[line width=2,darkgray!50] (p-44) -- (p-42); \draw[line width=2,darkgray!50] (p-44) -- (p-43); \draw[line width=2,darkgray!50] (p-44) -- (p-46); \draw[line width=2,darkgray!50] (p-45) -- (p-44); \draw[line width=2,darkgray!50] (p-45) -- (p-43); \draw[line width=2,darkgray!50] (p-45) -- (p-59); \draw[line width=2,darkgray!50] (p-45) -- (p-46); \draw[line width=2,darkgray!50] (p-46) -- (p-47); \draw[line width=2,darkgray!50] (p-46) -- (p-48); \draw[line width=2,darkgray!50] (p-47) -- (p-49); \draw[line width=2,darkgray!50] (p-48) -- (p-5); \draw[line width=2,darkgray!50] (p-49) -- (p-60); \draw[line width=2,darkgray!50] (p-49) -- (p-5); \draw[line width=2,darkgray!50] (p-50) -- (p-3); \draw[line width=2,darkgray!50] (p-50) -- (p-60); \draw[line width=2,darkgray!50] (p-51) -- (p-8); \draw[line width=2,darkgray!50] (p-51) -- (p-50); \draw[line width=2,darkgray!50] (p-52) -- (p-12); \draw[line width=2,darkgray!50] (p-52) -- (p-61); \draw[line width=2,darkgray!50] (p-53) -- (p-52); \draw[line width=2,darkgray!50] (p-54) -- (p-20); \draw[line width=2,darkgray!50] (p-55) -- (p-24); \draw[line width=2,darkgray!50] (p-55) -- (p-54); \draw[line width=2,darkgray!50] (p-56) -- (p-33); \draw[line width=2,darkgray!50] (p-56) -- (p-28); \draw[line width=2,darkgray!50] (p-56) -- (p-66); \draw[line width=2,darkgray!50] (p-57) -- (p-37); \draw[line width=2,darkgray!50] (p-57) -- (p-66); \draw[line width=2,darkgray!50] (p-58) -- (p-41); \draw[line width=2,darkgray!50] (p-58) -- (p-57); \draw[line width=2,darkgray!50] (p-59) -- (p-47); \draw[line width=2,darkgray!50] (p-59) -- (p-58); \draw[line width=2,darkgray!50] (p-60) -- (p-4); \draw[line width=2,darkgray!50] (p-61) -- (p-51); \draw[line width=2,darkgray!50] (p-61) -- (p-63); \draw[line width=2,darkgray!50] (p-66) -- (p-63); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/2.87/3.23, 62/2.87/4.23, 63/3.73/3.73, 64/3.73/2.73, 65/4.60/3.23, 66/4.60/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,red!50] (p-2) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-2); \draw[line width=2,red!50] (p-4) -- (p-3); \draw[line width=2,red!50] (p-4) -- (p-2); \draw[line width=2,red!50] (p-5) -- (p-4); \draw[line width=2,red!50] (p-5) -- (p-2); \draw[line width=2,red!50] (p-6) -- (p-1); \draw[line width=2,red!50] (p-6) -- (p-50); \draw[line width=2,red!50] (p-7) -- (p-1); \draw[line width=2,red!50] (p-7) -- (p-6); \draw[line width=2,red!50] (p-8) -- (p-7); \draw[line width=2,red!50] (p-8) -- (p-6); \draw[line width=2,red!50] (p-9) -- (p-7); \draw[line width=2,red!50] (p-9) -- (p-8); \draw[line width=2,red!50] (p-10) -- (p-9); \draw[line width=2,red!50] (p-10) -- (p-51); \draw[line width=2,red!50] (p-11) -- (p-9); \draw[line width=2,red!50] (p-11) -- (p-10); \draw[line width=2,red!50] (p-12) -- (p-11); \draw[line width=2,red!50] (p-12) -- (p-10); \draw[line width=2,red!50] (p-13) -- (p-11); \draw[line width=2,red!50] (p-13) -- (p-12); \draw[line width=2,red!50] (p-14) -- (p-13); \draw[line width=2,red!50] (p-14) -- (p-52); \draw[line width=2,red!50] (p-15) -- (p-13); \draw[line width=2,red!50] (p-15) -- (p-14); \draw[line width=2,red!50] (p-16) -- (p-15); \draw[line width=2,red!50] (p-16) -- (p-14); \draw[line width=2,red!50] (p-16) -- (p-53); \draw[line width=2,red!50] (p-17) -- (p-15); \draw[line width=2,red!50] (p-17) -- (p-16); \draw[line width=2,red!50] (p-18) -- (p-17); \draw[line width=2,red!50] (p-18) -- (p-53); \draw[line width=2,red!50] (p-19) -- (p-17); \draw[line width=2,red!50] (p-19) -- (p-18); \draw[line width=2,red!50] (p-20) -- (p-19); \draw[line width=2,red!50] (p-20) -- (p-18); \draw[line width=2,red!50] (p-21) -- (p-19); \draw[line width=2,red!50] (p-21) -- (p-20); \draw[line width=2,red!50] (p-22) -- (p-21); \draw[line width=2,red!50] (p-22) -- (p-54); \draw[line width=2,red!50] (p-23) -- (p-21); \draw[line width=2,red!50] (p-23) -- (p-22); \draw[line width=2,red!50] (p-24) -- (p-23); \draw[line width=2,red!50] (p-24) -- (p-22); \draw[line width=2,red!50] (p-25) -- (p-23); \draw[line width=2,red!50] (p-25) -- (p-24); \draw[line width=2,red!50] (p-26) -- (p-25); \draw[line width=2,red!50] (p-26) -- (p-55); \draw[line width=2,red!50] (p-27) -- (p-25); \draw[line width=2,red!50] (p-27) -- (p-26); \draw[line width=2,red!50] (p-28) -- (p-29); \draw[line width=2,red!50] (p-28) -- (p-55); \draw[line width=2,red!50] (p-29) -- (p-27); \draw[line width=2,red!50] (p-29) -- (p-26); \draw[line width=2,red!50] (p-30) -- (p-27); \draw[line width=2,red!50] (p-30) -- (p-29); \draw[line width=2,red!50] (p-31) -- (p-30); \draw[line width=2,red!50] (p-31) -- (p-28); \draw[line width=2,red!50] (p-32) -- (p-30); \draw[line width=2,red!50] (p-32) -- (p-31); \draw[line width=2,red!50] (p-33) -- (p-32); \draw[line width=2,red!50] (p-33) -- (p-31); \draw[line width=2,red!50] (p-34) -- (p-32); \draw[line width=2,red!50] (p-34) -- (p-33); \draw[line width=2,red!50] (p-35) -- (p-34); \draw[line width=2,red!50] (p-35) -- (p-56); \draw[line width=2,red!50] (p-36) -- (p-34); \draw[line width=2,red!50] (p-36) -- (p-35); \draw[line width=2,red!50] (p-37) -- (p-36); \draw[line width=2,red!50] (p-37) -- (p-35); \draw[line width=2,red!50] (p-38) -- (p-36); \draw[line width=2,red!50] (p-38) -- (p-37); \draw[line width=2,red!50] (p-39) -- (p-38); \draw[line width=2,red!50] (p-39) -- (p-57); \draw[line width=2,red!50] (p-40) -- (p-38); \draw[line width=2,red!50] (p-40) -- (p-39); \draw[line width=2,red!50] (p-41) -- (p-40); \draw[line width=2,red!50] (p-41) -- (p-39); \draw[line width=2,red!50] (p-42) -- (p-40); \draw[line width=2,red!50] (p-42) -- (p-41); \draw[line width=2,red!50] (p-43) -- (p-42); \draw[line width=2,red!50] (p-43) -- (p-58); \draw[line width=2,red!50] (p-44) -- (p-42); \draw[line width=2,red!50] (p-44) -- (p-43); \draw[line width=2,red!50] (p-44) -- (p-46); \draw[line width=2,red!50] (p-45) -- (p-44); \draw[line width=2,red!50] (p-45) -- (p-43); \draw[line width=2,red!50] (p-45) -- (p-59); \draw[line width=2,red!50] (p-45) -- (p-46); \draw[line width=2,red!50] (p-46) -- (p-47); \draw[line width=2,red!50] (p-46) -- (p-48); \draw[line width=2,red!50] (p-47) -- (p-49); \draw[line width=2,red!50] (p-47) -- (p-48); \draw[line width=2,red!50] (p-48) -- (p-49); \draw[line width=2,red!50] (p-48) -- (p-5); \draw[line width=2,red!50] (p-49) -- (p-60); \draw[line width=2,red!50] (p-49) -- (p-5); \draw[line width=2,red!50] (p-50) -- (p-3); \draw[line width=2,red!50] (p-50) -- (p-60); \draw[line width=2,red!50] (p-51) -- (p-8); \draw[line width=2,red!50] (p-51) -- (p-50); \draw[line width=2,red!50] (p-52) -- (p-12); \draw[line width=2,red!50] (p-53) -- (p-52); \draw[line width=2,red!50] (p-53) -- (p-62); \draw[line width=2,red!50] (p-54) -- (p-20); \draw[line width=2,red!50] (p-54) -- (p-62); \draw[line width=2,red!50] (p-55) -- (p-24); \draw[line width=2,red!50] (p-55) -- (p-54); \draw[line width=2,red!50] (p-56) -- (p-33); \draw[line width=2,red!50] (p-56) -- (p-28); \draw[line width=2,red!50] (p-56) -- (p-66); \draw[line width=2,red!50] (p-57) -- (p-37); \draw[line width=2,red!50] (p-57) -- (p-66); \draw[line width=2,red!50] (p-58) -- (p-41); \draw[line width=2,red!50] (p-58) -- (p-57); \draw[line width=2,red!50] (p-59) -- (p-47); \draw[line width=2,red!50] (p-59) -- (p-58); \draw[line width=2,red!50] (p-59) -- (p-65); \draw[line width=2,red!50] (p-60) -- (p-4); \draw[line width=2,red!50] (p-62) -- (p-63); \draw[line width=2,red!50] (p-63) -- (p-65); \draw[line width=2,red!50] (p-66) -- (p-65); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ #2351 $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/7.46/4.73, 2/6.96/5.60, 3/6.46/4.73, 4/5.96/5.60, 5/6.46/6.46, 6/6.60/4.23, 7/7.46/3.73, 8/6.60/3.23, 9/7.46/2.73, 10/6.46/2.73, 11/6.96/1.87, 12/5.96/1.87, 13/6.46/1.00, 14/5.60/1.50, 15/5.60/0.50, 16/4.73/1.00, 17/4.73/0.00, 18/4.23/0.87, 19/3.73/0.00, 20/3.23/0.87, 21/2.73/0.00, 22/2.73/1.00, 23/1.87/0.50, 24/1.87/1.50, 25/1.00/1.00, 26/1.50/1.87, 27/0.50/1.87, 28/1.87/3.23, 29/1.00/2.73, 30/0.00/2.73, 31/0.87/3.23, 32/0.00/3.73, 33/0.87/4.23, 34/0.00/4.73, 35/1.00/4.73, 36/0.50/5.60, 37/1.50/5.60, 38/1.00/6.46, 39/1.87/5.96, 40/1.87/6.96, 41/2.73/6.46, 42/2.73/7.46, 43/3.23/6.60, 44/3.73/7.46, 45/4.23/6.60, 46/4.73/7.46, 47/4.73/6.46, 48/5.60/6.96, 49/5.60/5.96, 50/5.60/4.23, 51/5.60/3.23, 52/5.10/2.37, 53/4.23/1.87, 54/3.23/1.87, 55/2.37/2.37, 56/1.87/4.23, 57/2.37/5.10, 58/3.23/5.60, 59/4.23/5.60, 60/5.10/5.10, 61/3.23/2.87, 62/3.73/3.73, 63/4.60/4.23, 64/3.73/4.73, 65/2.87/4.23, 66/4.73/3.73, 67/4.23/2.87, 68/2.73/3.73} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-2) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-2); \draw[line width=2,blue!50] (p-4) -- (p-3); \draw[line width=2,blue!50] (p-4) -- (p-2); \draw[line width=2,blue!50] (p-5) -- (p-4); \draw[line width=2,blue!50] (p-5) -- (p-2); \draw[line width=2,blue!50] (p-6) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-6); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-6); \draw[line width=2,blue!50] (p-9) -- (p-8); \draw[line width=2,blue!50] (p-10) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-12) -- (p-11); \draw[line width=2,blue!50] (p-12) -- (p-10); \draw[line width=2,blue!50] (p-13) -- (p-11); \draw[line width=2,blue!50] (p-13) -- (p-12); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-14) -- (p-52); \draw[line width=2,blue!50] (p-15) -- (p-14); \draw[line width=2,blue!50] (p-16) -- (p-15); \draw[line width=2,blue!50] (p-16) -- (p-14); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-18) -- (p-17); \draw[line width=2,blue!50] (p-18) -- (p-53); \draw[line width=2,blue!50] (p-19) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-19); \draw[line width=2,blue!50] (p-20) -- (p-18); \draw[line width=2,blue!50] (p-21) -- (p-19); \draw[line width=2,blue!50] (p-21) -- (p-20); \draw[line width=2,blue!50] (p-22) -- (p-21); \draw[line width=2,blue!50] (p-22) -- (p-54); \draw[line width=2,blue!50] (p-23) -- (p-21); \draw[line width=2,blue!50] (p-24) -- (p-22); \draw[line width=2,blue!50] (p-25) -- (p-23); \draw[line width=2,blue!50] (p-25) -- (p-24); \draw[line width=2,blue!50] (p-26) -- (p-25); \draw[line width=2,blue!50] (p-26) -- (p-55); \draw[line width=2,blue!50] (p-27) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-26); \draw[line width=2,blue!50] (p-28) -- (p-55); \draw[line width=2,blue!50] (p-28) -- (p-29); \draw[line width=2,blue!50] (p-29) -- (p-27); \draw[line width=2,blue!50] (p-29) -- (p-26); \draw[line width=2,blue!50] (p-30) -- (p-27); \draw[line width=2,blue!50] (p-30) -- (p-29); \draw[line width=2,blue!50] (p-31) -- (p-30); \draw[line width=2,blue!50] (p-31) -- (p-28); \draw[line width=2,blue!50] (p-32) -- (p-30); \draw[line width=2,blue!50] (p-32) -- (p-31); \draw[line width=2,blue!50] (p-33) -- (p-32); \draw[line width=2,blue!50] (p-33) -- (p-31); \draw[line width=2,blue!50] (p-34) -- (p-33); \draw[line width=2,blue!50] (p-35) -- (p-34); \draw[line width=2,blue!50] (p-36) -- (p-34); \draw[line width=2,blue!50] (p-36) -- (p-35); \draw[line width=2,blue!50] (p-37) -- (p-36); \draw[line width=2,blue!50] (p-37) -- (p-35); \draw[line width=2,blue!50] (p-38) -- (p-36); \draw[line width=2,blue!50] (p-38) -- (p-37); \draw[line width=2,blue!50] (p-39) -- (p-38); \draw[line width=2,blue!50] (p-40) -- (p-39); \draw[line width=2,blue!50] (p-41) -- (p-40); \draw[line width=2,blue!50] (p-41) -- (p-39); \draw[line width=2,blue!50] (p-42) -- (p-40); \draw[line width=2,blue!50] (p-42) -- (p-41); \draw[line width=2,blue!50] (p-42) -- (p-44); \draw[line width=2,blue!50] (p-43) -- (p-44); \draw[line width=2,blue!50] (p-43) -- (p-42); \draw[line width=2,blue!50] (p-44) -- (p-46); \draw[line width=2,blue!50] (p-45) -- (p-46); \draw[line width=2,blue!50] (p-45) -- (p-43); \draw[line width=2,blue!50] (p-45) -- (p-44); \draw[line width=2,blue!50] (p-46) -- (p-48); \draw[line width=2,blue!50] (p-47) -- (p-48); \draw[line width=2,blue!50] (p-47) -- (p-46); \draw[line width=2,blue!50] (p-48) -- (p-5); \draw[line width=2,blue!50] (p-49) -- (p-60); \draw[line width=2,blue!50] (p-49) -- (p-5); \draw[line width=2,blue!50] (p-49) -- (p-47); \draw[line width=2,blue!50] (p-49) -- (p-48); \draw[line width=2,blue!50] (p-50) -- (p-6); \draw[line width=2,blue!50] (p-50) -- (p-3); \draw[line width=2,blue!50] (p-51) -- (p-10); \draw[line width=2,blue!50] (p-51) -- (p-8); \draw[line width=2,blue!50] (p-52) -- (p-12); \draw[line width=2,blue!50] (p-52) -- (p-51); \draw[line width=2,blue!50] (p-53) -- (p-16); \draw[line width=2,blue!50] (p-54) -- (p-20); \draw[line width=2,blue!50] (p-54) -- (p-53); \draw[line width=2,blue!50] (p-55) -- (p-24); \draw[line width=2,blue!50] (p-55) -- (p-61); \draw[line width=2,blue!50] (p-56) -- (p-33); \draw[line width=2,blue!50] (p-57) -- (p-39); \draw[line width=2,blue!50] (p-57) -- (p-37); \draw[line width=2,blue!50] (p-57) -- (p-58); \draw[line width=2,blue!50] (p-58) -- (p-43); \draw[line width=2,blue!50] (p-58) -- (p-41); \draw[line width=2,blue!50] (p-58) -- (p-64); \draw[line width=2,blue!50] (p-59) -- (p-47); \draw[line width=2,blue!50] (p-59) -- (p-45); \draw[line width=2,blue!50] (p-59) -- (p-60); \draw[line width=2,blue!50] (p-60) -- (p-63); \draw[line width=2,blue!50] (p-60) -- (p-4); \draw[line width=2,blue!50] (p-61) -- (p-54); \draw[line width=2,blue!50] (p-61) -- (p-62); \draw[line width=2,blue!50] (p-62) -- (p-66); \draw[line width=2,blue!50] (p-62) -- (p-65); \draw[line width=2,blue!50] (p-63) -- (p-62); \draw[line width=2,blue!50] (p-63) -- (p-50); \draw[line width=2,blue!50] (p-64) -- (p-63); \draw[line width=2,blue!50] (p-64) -- (p-65); \draw[line width=2,blue!50] (p-65) -- (p-57); \draw[line width=2,blue!50] (p-65) -- (p-56); \draw[line width=2,blue!50] (p-66) -- (p-51); \draw[line width=2,blue!50] (p-66) -- (p-50); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 14/52, 15/13, 15/14, 16/15, 16/14, 17/15, 17/16, 18/17, 18/53, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 22/54, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 26/55, 27/25, 27/26, 28/55, 28/68, 28/29, 29/27, 29/26, 30/27, 30/29, 31/30, 31/28, 32/30, 32/31, 33/32, 33/31, 34/32, 34/33, 35/34, 35/56, 36/34, 36/35, 37/36, 37/35, 38/36, 38/37, 39/38, 40/38, 40/39, 41/40, 41/39, 42/40, 42/41, 42/44, 43/44, 43/42, 44/46, 45/46, 45/43, 45/44, 46/48, 47/48, 47/46, 48/5, 49/60, 49/5, 49/47, 49/48, 50/6, 50/3, 51/10, 51/8, 52/12, 52/51, 53/16, 53/67, 54/20, 54/53, 55/24, 55/61, 56/33, 56/68, 57/39, 57/37, 57/58, 58/43, 58/41, 58/64, 59/47, 59/45, 59/60, 60/63, 60/4, 61/54, 61/62, 62/66, 62/65, 63/62, 63/50, 64/63, 64/59, 64/65, 65/57, 65/56, 66/51, 66/50, 67/52, 67/62, 67/66, 68/61, 68/62} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/330, 2/90, 3/270, 4/210, 5/360, 6/180, 7/60, 8/240, 9/30, 10/90, 11/330, 12/150, 13/360, 14/60, 15/360, 16/180, 17/240, 18/30, 19/330, 20/90, 21/300, 22/360, 23/300, 24/120, 25/180, 26/330, 27/270, 28/78, 29/90, 30/150, 31/300, 32/240, 33/60, 34/120, 35/330, 36/150, 37/330, 38/180, 39/240, 40/180, 41/360, 42/60, 43/270, 44/30, 45/270, 46/120, 47/180, 48/60, 49/300, 50/108, 51/18, 52/198, 53/48, 54/228, 55/258, 56/258, 57/258, 58/78, 59/108, 60/288, 61/270, 62/30, 63/213, 64/273, 65/183, 66/30, 67/270, 68/150} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/7.46/4.73, 2/6.96/5.60, 3/6.46/4.73, 4/5.96/5.60, 5/6.46/6.46, 6/6.60/4.23, 7/7.46/3.73, 8/6.60/3.23, 9/7.46/2.73, 10/6.46/2.73, 11/6.96/1.87, 12/5.96/1.87, 13/6.46/1.00, 14/5.60/1.50, 15/5.60/0.50, 16/4.73/1.00, 17/4.73/0.00, 18/4.23/0.87, 19/3.73/0.00, 20/3.23/0.87, 21/2.73/0.00, 22/2.73/1.00, 23/1.87/0.50, 24/1.87/1.50, 25/1.00/1.00, 26/1.50/1.87, 27/0.50/1.87, 28/1.87/3.23, 29/1.00/2.73, 30/0.00/2.73, 31/0.87/3.23, 32/0.00/3.73, 33/0.87/4.23, 34/0.00/4.73, 35/1.00/4.73, 36/0.50/5.60, 37/1.50/5.60, 38/1.00/6.46, 39/1.87/5.96, 40/1.87/6.96, 41/2.73/6.46, 42/2.73/7.46, 43/3.23/6.60, 44/3.73/7.46, 45/4.23/6.60, 46/4.73/7.46, 47/4.73/6.46, 48/5.60/6.96, 49/5.60/5.96, 50/5.60/4.23, 51/5.60/3.23, 52/5.10/2.37, 53/4.23/1.87, 54/3.23/1.87, 55/2.37/2.37, 56/1.87/4.23, 57/2.37/5.10, 58/3.23/5.60, 59/4.23/5.60, 60/5.10/5.10, 61/3.23/2.87, 62/3.73/3.73, 63/4.60/4.23, 64/3.73/4.73, 65/2.87/4.23, 66/4.73/3.73, 67/4.23/2.87, 68/2.73/3.73} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,orange!50] (p-2) -- (p-1); \draw[line width=2,orange!50] (p-3) -- (p-1); \draw[line width=2,orange!50] (p-3) -- (p-2); \draw[line width=2,orange!50] (p-4) -- (p-3); \draw[line width=2,orange!50] (p-4) -- (p-2); \draw[line width=2,orange!50] (p-5) -- (p-4); \draw[line width=2,orange!50] (p-5) -- (p-2); \draw[line width=2,orange!50] (p-6) -- (p-1); \draw[line width=2,orange!50] (p-7) -- (p-1); \draw[line width=2,orange!50] (p-7) -- (p-6); \draw[line width=2,orange!50] (p-8) -- (p-7); \draw[line width=2,orange!50] (p-8) -- (p-6); \draw[line width=2,orange!50] (p-9) -- (p-7); \draw[line width=2,orange!50] (p-9) -- (p-8); \draw[line width=2,orange!50] (p-10) -- (p-9); \draw[line width=2,orange!50] (p-11) -- (p-9); \draw[line width=2,orange!50] (p-11) -- (p-10); \draw[line width=2,orange!50] (p-12) -- (p-11); \draw[line width=2,orange!50] (p-12) -- (p-10); \draw[line width=2,orange!50] (p-13) -- (p-11); \draw[line width=2,orange!50] (p-13) -- (p-12); \draw[line width=2,orange!50] (p-14) -- (p-13); \draw[line width=2,orange!50] (p-14) -- (p-52); \draw[line width=2,orange!50] (p-15) -- (p-13); \draw[line width=2,orange!50] (p-15) -- (p-14); \draw[line width=2,orange!50] (p-16) -- (p-15); \draw[line width=2,orange!50] (p-16) -- (p-14); \draw[line width=2,orange!50] (p-17) -- (p-15); \draw[line width=2,orange!50] (p-17) -- (p-16); \draw[line width=2,orange!50] (p-18) -- (p-17); \draw[line width=2,orange!50] (p-18) -- (p-53); \draw[line width=2,orange!50] (p-19) -- (p-17); \draw[line width=2,orange!50] (p-19) -- (p-18); \draw[line width=2,orange!50] (p-20) -- (p-19); \draw[line width=2,orange!50] (p-20) -- (p-18); \draw[line width=2,orange!50] (p-21) -- (p-19); \draw[line width=2,orange!50] (p-21) -- (p-20); \draw[line width=2,orange!50] (p-22) -- (p-21); \draw[line width=2,orange!50] (p-22) -- (p-54); \draw[line width=2,orange!50] (p-23) -- (p-21); \draw[line width=2,orange!50] (p-23) -- (p-22); \draw[line width=2,orange!50] (p-24) -- (p-23); \draw[line width=2,orange!50] (p-24) -- (p-22); \draw[line width=2,orange!50] (p-25) -- (p-23); \draw[line width=2,orange!50] (p-25) -- (p-24); \draw[line width=2,orange!50] (p-26) -- (p-25); \draw[line width=2,orange!50] (p-26) -- (p-55); \draw[line width=2,orange!50] (p-27) -- (p-25); \draw[line width=2,orange!50] (p-27) -- (p-26); \draw[line width=2,orange!50] (p-28) -- (p-55); \draw[line width=2,orange!50] (p-28) -- (p-29); \draw[line width=2,orange!50] (p-29) -- (p-27); \draw[line width=2,orange!50] (p-29) -- (p-26); \draw[line width=2,orange!50] (p-30) -- (p-27); \draw[line width=2,orange!50] (p-30) -- (p-29); \draw[line width=2,orange!50] (p-31) -- (p-30); \draw[line width=2,orange!50] (p-31) -- (p-28); \draw[line width=2,orange!50] (p-32) -- (p-30); \draw[line width=2,orange!50] (p-32) -- (p-31); \draw[line width=2,orange!50] (p-33) -- (p-32); \draw[line width=2,orange!50] (p-33) -- (p-31); \draw[line width=2,orange!50] (p-34) -- (p-32); \draw[line width=2,orange!50] (p-34) -- (p-33); \draw[line width=2,orange!50] (p-35) -- (p-34); \draw[line width=2,orange!50] (p-36) -- (p-34); \draw[line width=2,orange!50] (p-36) -- (p-35); \draw[line width=2,orange!50] (p-37) -- (p-36); \draw[line width=2,orange!50] (p-37) -- (p-35); \draw[line width=2,orange!50] (p-38) -- (p-36); \draw[line width=2,orange!50] (p-38) -- (p-37); \draw[line width=2,orange!50] (p-39) -- (p-38); \draw[line width=2,orange!50] (p-40) -- (p-38); \draw[line width=2,orange!50] (p-41) -- (p-39); \draw[line width=2,orange!50] (p-42) -- (p-40); \draw[line width=2,orange!50] (p-42) -- (p-41); \draw[line width=2,orange!50] (p-42) -- (p-44); \draw[line width=2,orange!50] (p-43) -- (p-44); \draw[line width=2,orange!50] (p-43) -- (p-42); \draw[line width=2,orange!50] (p-44) -- (p-46); \draw[line width=2,orange!50] (p-45) -- (p-46); \draw[line width=2,orange!50] (p-45) -- (p-43); \draw[line width=2,orange!50] (p-45) -- (p-44); \draw[line width=2,orange!50] (p-46) -- (p-48); \draw[line width=2,orange!50] (p-47) -- (p-48); \draw[line width=2,orange!50] (p-47) -- (p-46); \draw[line width=2,orange!50] (p-48) -- (p-5); \draw[line width=2,orange!50] (p-49) -- (p-60); \draw[line width=2,orange!50] (p-49) -- (p-5); \draw[line width=2,orange!50] (p-49) -- (p-47); \draw[line width=2,orange!50] (p-49) -- (p-48); \draw[line width=2,orange!50] (p-50) -- (p-6); \draw[line width=2,orange!50] (p-50) -- (p-3); \draw[line width=2,orange!50] (p-51) -- (p-10); \draw[line width=2,orange!50] (p-51) -- (p-8); \draw[line width=2,orange!50] (p-52) -- (p-12); \draw[line width=2,orange!50] (p-52) -- (p-51); \draw[line width=2,orange!50] (p-53) -- (p-16); \draw[line width=2,orange!50] (p-53) -- (p-67); \draw[line width=2,orange!50] (p-54) -- (p-20); \draw[line width=2,orange!50] (p-54) -- (p-53); \draw[line width=2,orange!50] (p-55) -- (p-24); \draw[line width=2,orange!50] (p-55) -- (p-61); \draw[line width=2,orange!50] (p-57) -- (p-39); \draw[line width=2,orange!50] (p-57) -- (p-37); \draw[line width=2,orange!50] (p-57) -- (p-58); \draw[line width=2,orange!50] (p-58) -- (p-43); \draw[line width=2,orange!50] (p-58) -- (p-41); \draw[line width=2,orange!50] (p-58) -- (p-64); \draw[line width=2,orange!50] (p-59) -- (p-47); \draw[line width=2,orange!50] (p-60) -- (p-63); \draw[line width=2,orange!50] (p-61) -- (p-54); \draw[line width=2,orange!50] (p-61) -- (p-62); \draw[line width=2,orange!50] (p-62) -- (p-66); \draw[line width=2,orange!50] (p-62) -- (p-65); \draw[line width=2,orange!50] (p-63) -- (p-62); \draw[line width=2,orange!50] (p-63) -- (p-50); \draw[line width=2,orange!50] (p-64) -- (p-63); \draw[line width=2,orange!50] (p-64) -- (p-59); \draw[line width=2,orange!50] (p-64) -- (p-65); \draw[line width=2,orange!50] (p-65) -- (p-57); \draw[line width=2,orange!50] (p-66) -- (p-51); \draw[line width=2,orange!50] (p-66) -- (p-50); \draw[line width=2,orange!50] (p-67) -- (p-52); \draw[line width=2,orange!50] (p-67) -- (p-62); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/7.46/4.73, 2/6.96/5.60, 3/6.46/4.73, 4/5.96/5.60, 5/6.46/6.46, 6/6.60/4.23, 7/7.46/3.73, 8/6.60/3.23, 9/7.46/2.73, 10/6.46/2.73, 11/6.96/1.87, 12/5.96/1.87, 13/6.46/1.00, 14/5.60/1.50, 15/5.60/0.50, 16/4.73/1.00, 17/4.73/0.00, 18/4.23/0.87, 19/3.73/0.00, 20/3.23/0.87, 21/2.73/0.00, 22/2.73/1.00, 23/1.87/0.50, 24/1.87/1.50, 25/1.00/1.00, 26/1.50/1.87, 27/0.50/1.87, 28/1.87/3.23, 29/1.00/2.73, 30/0.00/2.73, 31/0.87/3.23, 32/0.00/3.73, 33/0.87/4.23, 34/0.00/4.73, 35/1.00/4.73, 36/0.50/5.60, 37/1.50/5.60, 38/1.00/6.46, 39/1.87/5.96, 40/1.87/6.96, 41/2.73/6.46, 42/2.73/7.46, 43/3.23/6.60, 44/3.73/7.46, 45/4.23/6.60, 46/4.73/7.46, 47/4.73/6.46, 48/5.60/6.96, 49/5.60/5.96, 50/5.60/4.23, 51/5.60/3.23, 52/5.10/2.37, 53/4.23/1.87, 54/3.23/1.87, 55/2.37/2.37, 56/1.87/4.23, 57/2.37/5.10, 58/3.23/5.60, 59/4.23/5.60, 60/5.10/5.10, 61/3.23/2.87, 62/3.73/3.73, 63/4.60/4.23, 64/3.73/4.73, 65/2.87/4.23, 66/4.73/3.73, 67/4.23/2.87, 68/2.73/3.73} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,green!50] (p-3) -- (p-1); \draw[line width=2,green!50] (p-3) -- (p-2); \draw[line width=2,green!50] (p-4) -- (p-3); \draw[line width=2,green!50] (p-4) -- (p-2); \draw[line width=2,green!50] (p-5) -- (p-4); \draw[line width=2,green!50] (p-5) -- (p-2); \draw[line width=2,green!50] (p-6) -- (p-1); \draw[line width=2,green!50] (p-7) -- (p-1); \draw[line width=2,green!50] (p-7) -- (p-6); \draw[line width=2,green!50] (p-8) -- (p-7); \draw[line width=2,green!50] (p-8) -- (p-6); \draw[line width=2,green!50] (p-9) -- (p-7); \draw[line width=2,green!50] (p-9) -- (p-8); \draw[line width=2,green!50] (p-10) -- (p-9); \draw[line width=2,green!50] (p-11) -- (p-10); \draw[line width=2,green!50] (p-12) -- (p-11); \draw[line width=2,green!50] (p-12) -- (p-10); \draw[line width=2,green!50] (p-13) -- (p-11); \draw[line width=2,green!50] (p-13) -- (p-12); \draw[line width=2,green!50] (p-14) -- (p-13); \draw[line width=2,green!50] (p-14) -- (p-52); \draw[line width=2,green!50] (p-15) -- (p-13); \draw[line width=2,green!50] (p-15) -- (p-14); \draw[line width=2,green!50] (p-16) -- (p-15); \draw[line width=2,green!50] (p-16) -- (p-14); \draw[line width=2,green!50] (p-17) -- (p-16); \draw[line width=2,green!50] (p-18) -- (p-17); \draw[line width=2,green!50] (p-18) -- (p-53); \draw[line width=2,green!50] (p-19) -- (p-17); \draw[line width=2,green!50] (p-19) -- (p-18); \draw[line width=2,green!50] (p-20) -- (p-19); \draw[line width=2,green!50] (p-20) -- (p-18); \draw[line width=2,green!50] (p-21) -- (p-19); \draw[line width=2,green!50] (p-21) -- (p-20); \draw[line width=2,green!50] (p-22) -- (p-21); \draw[line width=2,green!50] (p-22) -- (p-54); \draw[line width=2,green!50] (p-23) -- (p-22); \draw[line width=2,green!50] (p-24) -- (p-23); \draw[line width=2,green!50] (p-24) -- (p-22); \draw[line width=2,green!50] (p-25) -- (p-23); \draw[line width=2,green!50] (p-25) -- (p-24); \draw[line width=2,green!50] (p-26) -- (p-25); \draw[line width=2,green!50] (p-26) -- (p-55); \draw[line width=2,green!50] (p-27) -- (p-25); \draw[line width=2,green!50] (p-27) -- (p-26); \draw[line width=2,green!50] (p-29) -- (p-27); \draw[line width=2,green!50] (p-29) -- (p-26); \draw[line width=2,green!50] (p-30) -- (p-27); \draw[line width=2,green!50] (p-30) -- (p-29); \draw[line width=2,green!50] (p-32) -- (p-30); \draw[line width=2,green!50] (p-34) -- (p-32); \draw[line width=2,green!50] (p-35) -- (p-34); \draw[line width=2,green!50] (p-36) -- (p-34); \draw[line width=2,green!50] (p-36) -- (p-35); \draw[line width=2,green!50] (p-37) -- (p-36); \draw[line width=2,green!50] (p-37) -- (p-35); \draw[line width=2,green!50] (p-38) -- (p-36); \draw[line width=2,green!50] (p-38) -- (p-37); \draw[line width=2,green!50] (p-39) -- (p-38); \draw[line width=2,green!50] (p-40) -- (p-38); \draw[line width=2,green!50] (p-40) -- (p-39); \draw[line width=2,green!50] (p-41) -- (p-40); \draw[line width=2,green!50] (p-41) -- (p-39); \draw[line width=2,green!50] (p-42) -- (p-40); \draw[line width=2,green!50] (p-42) -- (p-41); \draw[line width=2,green!50] (p-42) -- (p-44); \draw[line width=2,green!50] (p-43) -- (p-44); \draw[line width=2,green!50] (p-43) -- (p-42); \draw[line width=2,green!50] (p-44) -- (p-46); \draw[line width=2,green!50] (p-45) -- (p-46); \draw[line width=2,green!50] (p-45) -- (p-43); \draw[line width=2,green!50] (p-45) -- (p-44); \draw[line width=2,green!50] (p-46) -- (p-48); \draw[line width=2,green!50] (p-47) -- (p-48); \draw[line width=2,green!50] (p-47) -- (p-46); \draw[line width=2,green!50] (p-48) -- (p-5); \draw[line width=2,green!50] (p-49) -- (p-60); \draw[line width=2,green!50] (p-49) -- (p-5); \draw[line width=2,green!50] (p-49) -- (p-47); \draw[line width=2,green!50] (p-49) -- (p-48); \draw[line width=2,green!50] (p-50) -- (p-6); \draw[line width=2,green!50] (p-50) -- (p-3); \draw[line width=2,green!50] (p-51) -- (p-10); \draw[line width=2,green!50] (p-51) -- (p-8); \draw[line width=2,green!50] (p-52) -- (p-12); \draw[line width=2,green!50] (p-52) -- (p-51); \draw[line width=2,green!50] (p-53) -- (p-16); \draw[line width=2,green!50] (p-53) -- (p-67); \draw[line width=2,green!50] (p-54) -- (p-20); \draw[line width=2,green!50] (p-54) -- (p-53); \draw[line width=2,green!50] (p-55) -- (p-61); \draw[line width=2,green!50] (p-57) -- (p-39); \draw[line width=2,green!50] (p-57) -- (p-37); \draw[line width=2,green!50] (p-57) -- (p-58); \draw[line width=2,green!50] (p-58) -- (p-43); \draw[line width=2,green!50] (p-58) -- (p-41); \draw[line width=2,green!50] (p-58) -- (p-64); \draw[line width=2,green!50] (p-59) -- (p-47); \draw[line width=2,green!50] (p-59) -- (p-45); \draw[line width=2,green!50] (p-59) -- (p-60); \draw[line width=2,green!50] (p-60) -- (p-63); \draw[line width=2,green!50] (p-60) -- (p-4); \draw[line width=2,green!50] (p-61) -- (p-54); \draw[line width=2,green!50] (p-61) -- (p-62); \draw[line width=2,green!50] (p-62) -- (p-66); \draw[line width=2,green!50] (p-62) -- (p-65); \draw[line width=2,green!50] (p-63) -- (p-62); \draw[line width=2,green!50] (p-63) -- (p-50); \draw[line width=2,green!50] (p-64) -- (p-63); \draw[line width=2,green!50] (p-64) -- (p-59); \draw[line width=2,green!50] (p-64) -- (p-65); \draw[line width=2,green!50] (p-65) -- (p-57); \draw[line width=2,green!50] (p-66) -- (p-51); \draw[line width=2,green!50] (p-66) -- (p-50); \draw[line width=2,green!50] (p-67) -- (p-52); \draw[line width=2,green!50] (p-67) -- (p-66); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/7.46/4.73, 2/6.96/5.60, 3/6.46/4.73, 4/5.96/5.60, 5/6.46/6.46, 6/6.60/4.23, 7/7.46/3.73, 8/6.60/3.23, 9/7.46/2.73, 10/6.46/2.73, 11/6.96/1.87, 12/5.96/1.87, 13/6.46/1.00, 14/5.60/1.50, 15/5.60/0.50, 16/4.73/1.00, 17/4.73/0.00, 18/4.23/0.87, 19/3.73/0.00, 20/3.23/0.87, 21/2.73/0.00, 22/2.73/1.00, 23/1.87/0.50, 24/1.87/1.50, 25/1.00/1.00, 26/1.50/1.87, 27/0.50/1.87, 28/1.87/3.23, 29/1.00/2.73, 30/0.00/2.73, 31/0.87/3.23, 32/0.00/3.73, 33/0.87/4.23, 34/0.00/4.73, 35/1.00/4.73, 36/0.50/5.60, 37/1.50/5.60, 38/1.00/6.46, 39/1.87/5.96, 40/1.87/6.96, 41/2.73/6.46, 42/2.73/7.46, 43/3.23/6.60, 44/3.73/7.46, 45/4.23/6.60, 46/4.73/7.46, 47/4.73/6.46, 48/5.60/6.96, 49/5.60/5.96, 50/5.60/4.23, 51/5.60/3.23, 52/5.10/2.37, 53/4.23/1.87, 54/3.23/1.87, 55/2.37/2.37, 56/1.87/4.23, 57/2.37/5.10, 58/3.23/5.60, 59/4.23/5.60, 60/5.10/5.10, 61/3.23/2.87, 62/3.73/3.73, 63/4.60/4.23, 64/3.73/4.73, 65/2.87/4.23, 66/4.73/3.73, 67/4.23/2.87, 68/2.73/3.73} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,darkgray!50] (p-2) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-2); \draw[line width=2,darkgray!50] (p-4) -- (p-3); \draw[line width=2,darkgray!50] (p-4) -- (p-2); \draw[line width=2,darkgray!50] (p-5) -- (p-4); \draw[line width=2,darkgray!50] (p-5) -- (p-2); \draw[line width=2,darkgray!50] (p-6) -- (p-1); \draw[line width=2,darkgray!50] (p-7) -- (p-1); \draw[line width=2,darkgray!50] (p-8) -- (p-6); \draw[line width=2,darkgray!50] (p-9) -- (p-7); \draw[line width=2,darkgray!50] (p-9) -- (p-8); \draw[line width=2,darkgray!50] (p-10) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-10); \draw[line width=2,darkgray!50] (p-12) -- (p-11); \draw[line width=2,darkgray!50] (p-12) -- (p-10); \draw[line width=2,darkgray!50] (p-13) -- (p-11); \draw[line width=2,darkgray!50] (p-13) -- (p-12); \draw[line width=2,darkgray!50] (p-14) -- (p-13); \draw[line width=2,darkgray!50] (p-14) -- (p-52); \draw[line width=2,darkgray!50] (p-15) -- (p-13); \draw[line width=2,darkgray!50] (p-15) -- (p-14); \draw[line width=2,darkgray!50] (p-16) -- (p-15); \draw[line width=2,darkgray!50] (p-16) -- (p-14); \draw[line width=2,darkgray!50] (p-17) -- (p-16); \draw[line width=2,darkgray!50] (p-18) -- (p-17); \draw[line width=2,darkgray!50] (p-18) -- (p-53); \draw[line width=2,darkgray!50] (p-19) -- (p-17); \draw[line width=2,darkgray!50] (p-19) -- (p-18); \draw[line width=2,darkgray!50] (p-20) -- (p-19); \draw[line width=2,darkgray!50] (p-20) -- (p-18); \draw[line width=2,darkgray!50] (p-21) -- (p-19); \draw[line width=2,darkgray!50] (p-21) -- (p-20); \draw[line width=2,darkgray!50] (p-22) -- (p-21); \draw[line width=2,darkgray!50] (p-22) -- (p-54); \draw[line width=2,darkgray!50] (p-23) -- (p-22); \draw[line width=2,darkgray!50] (p-24) -- (p-23); \draw[line width=2,darkgray!50] (p-24) -- (p-22); \draw[line width=2,darkgray!50] (p-25) -- (p-23); \draw[line width=2,darkgray!50] (p-25) -- (p-24); \draw[line width=2,darkgray!50] (p-26) -- (p-25); \draw[line width=2,darkgray!50] (p-26) -- (p-55); \draw[line width=2,darkgray!50] (p-27) -- (p-25); \draw[line width=2,darkgray!50] (p-27) -- (p-26); \draw[line width=2,darkgray!50] (p-28) -- (p-55); \draw[line width=2,darkgray!50] (p-28) -- (p-68); \draw[line width=2,darkgray!50] (p-28) -- (p-29); \draw[line width=2,darkgray!50] (p-29) -- (p-27); \draw[line width=2,darkgray!50] (p-29) -- (p-26); \draw[line width=2,darkgray!50] (p-30) -- (p-27); \draw[line width=2,darkgray!50] (p-30) -- (p-29); \draw[line width=2,darkgray!50] (p-31) -- (p-30); \draw[line width=2,darkgray!50] (p-31) -- (p-28); \draw[line width=2,darkgray!50] (p-32) -- (p-30); \draw[line width=2,darkgray!50] (p-32) -- (p-31); \draw[line width=2,darkgray!50] (p-33) -- (p-32); \draw[line width=2,darkgray!50] (p-33) -- (p-31); \draw[line width=2,darkgray!50] (p-34) -- (p-32); \draw[line width=2,darkgray!50] (p-34) -- (p-33); \draw[line width=2,darkgray!50] (p-35) -- (p-34); \draw[line width=2,darkgray!50] (p-35) -- (p-56); \draw[line width=2,darkgray!50] (p-36) -- (p-34); \draw[line width=2,darkgray!50] (p-36) -- (p-35); \draw[line width=2,darkgray!50] (p-37) -- (p-36); \draw[line width=2,darkgray!50] (p-37) -- (p-35); \draw[line width=2,darkgray!50] (p-38) -- (p-36); \draw[line width=2,darkgray!50] (p-38) -- (p-37); \draw[line width=2,darkgray!50] (p-39) -- (p-38); \draw[line width=2,darkgray!50] (p-40) -- (p-38); \draw[line width=2,darkgray!50] (p-40) -- (p-39); \draw[line width=2,darkgray!50] (p-41) -- (p-40); \draw[line width=2,darkgray!50] (p-41) -- (p-39); \draw[line width=2,darkgray!50] (p-42) -- (p-40); \draw[line width=2,darkgray!50] (p-42) -- (p-41); \draw[line width=2,darkgray!50] (p-42) -- (p-44); \draw[line width=2,darkgray!50] (p-43) -- (p-44); \draw[line width=2,darkgray!50] (p-43) -- (p-42); \draw[line width=2,darkgray!50] (p-44) -- (p-46); \draw[line width=2,darkgray!50] (p-45) -- (p-46); \draw[line width=2,darkgray!50] (p-45) -- (p-43); \draw[line width=2,darkgray!50] (p-45) -- (p-44); \draw[line width=2,darkgray!50] (p-46) -- (p-48); \draw[line width=2,darkgray!50] (p-47) -- (p-48); \draw[line width=2,darkgray!50] (p-47) -- (p-46); \draw[line width=2,darkgray!50] (p-48) -- (p-5); \draw[line width=2,darkgray!50] (p-49) -- (p-60); \draw[line width=2,darkgray!50] (p-49) -- (p-5); \draw[line width=2,darkgray!50] (p-49) -- (p-47); \draw[line width=2,darkgray!50] (p-49) -- (p-48); \draw[line width=2,darkgray!50] (p-50) -- (p-6); \draw[line width=2,darkgray!50] (p-50) -- (p-3); \draw[line width=2,darkgray!50] (p-51) -- (p-10); \draw[line width=2,darkgray!50] (p-51) -- (p-8); \draw[line width=2,darkgray!50] (p-52) -- (p-12); \draw[line width=2,darkgray!50] (p-52) -- (p-51); \draw[line width=2,darkgray!50] (p-53) -- (p-16); \draw[line width=2,darkgray!50] (p-54) -- (p-20); \draw[line width=2,darkgray!50] (p-54) -- (p-53); \draw[line width=2,darkgray!50] (p-55) -- (p-24); \draw[line width=2,darkgray!50] (p-55) -- (p-61); \draw[line width=2,darkgray!50] (p-56) -- (p-68); \draw[line width=2,darkgray!50] (p-57) -- (p-39); \draw[line width=2,darkgray!50] (p-57) -- (p-37); \draw[line width=2,darkgray!50] (p-57) -- (p-58); \draw[line width=2,darkgray!50] (p-58) -- (p-43); \draw[line width=2,darkgray!50] (p-58) -- (p-41); \draw[line width=2,darkgray!50] (p-58) -- (p-64); \draw[line width=2,darkgray!50] (p-59) -- (p-47); \draw[line width=2,darkgray!50] (p-59) -- (p-45); \draw[line width=2,darkgray!50] (p-59) -- (p-60); \draw[line width=2,darkgray!50] (p-60) -- (p-63); \draw[line width=2,darkgray!50] (p-60) -- (p-4); \draw[line width=2,darkgray!50] (p-61) -- (p-54); \draw[line width=2,darkgray!50] (p-61) -- (p-62); \draw[line width=2,darkgray!50] (p-62) -- (p-66); \draw[line width=2,darkgray!50] (p-62) -- (p-65); \draw[line width=2,darkgray!50] (p-63) -- (p-62); \draw[line width=2,darkgray!50] (p-63) -- (p-50); \draw[line width=2,darkgray!50] (p-64) -- (p-63); \draw[line width=2,darkgray!50] (p-64) -- (p-59); \draw[line width=2,darkgray!50] (p-64) -- (p-65); \draw[line width=2,darkgray!50] (p-65) -- (p-57); \draw[line width=2,darkgray!50] (p-66) -- (p-51); \draw[line width=2,darkgray!50] (p-66) -- (p-50); \draw[line width=2,darkgray!50] (p-68) -- (p-61); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/7.46/4.73, 2/6.96/5.60, 3/6.46/4.73, 4/5.96/5.60, 5/6.46/6.46, 6/6.60/4.23, 7/7.46/3.73, 8/6.60/3.23, 9/7.46/2.73, 10/6.46/2.73, 11/6.96/1.87, 12/5.96/1.87, 13/6.46/1.00, 14/5.60/1.50, 15/5.60/0.50, 16/4.73/1.00, 17/4.73/0.00, 18/4.23/0.87, 19/3.73/0.00, 20/3.23/0.87, 21/2.73/0.00, 22/2.73/1.00, 23/1.87/0.50, 24/1.87/1.50, 25/1.00/1.00, 26/1.50/1.87, 27/0.50/1.87, 28/1.87/3.23, 29/1.00/2.73, 30/0.00/2.73, 31/0.87/3.23, 32/0.00/3.73, 33/0.87/4.23, 34/0.00/4.73, 35/1.00/4.73, 36/0.50/5.60, 37/1.50/5.60, 38/1.00/6.46, 39/1.87/5.96, 40/1.87/6.96, 41/2.73/6.46, 42/2.73/7.46, 43/3.23/6.60, 44/3.73/7.46, 45/4.23/6.60, 46/4.73/7.46, 47/4.73/6.46, 48/5.60/6.96, 49/5.60/5.96, 50/5.60/4.23, 51/5.60/3.23, 52/5.10/2.37, 53/4.23/1.87, 54/3.23/1.87, 55/2.37/2.37, 56/1.87/4.23, 57/2.37/5.10, 58/3.23/5.60, 59/4.23/5.60, 60/5.10/5.10, 61/3.23/2.87, 62/3.73/3.73, 63/4.60/4.23, 64/3.73/4.73, 65/2.87/4.23, 66/4.73/3.73, 67/4.23/2.87, 68/2.73/3.73} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,red!50] (p-2) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-2); \draw[line width=2,red!50] (p-4) -- (p-3); \draw[line width=2,red!50] (p-4) -- (p-2); \draw[line width=2,red!50] (p-5) -- (p-4); \draw[line width=2,red!50] (p-5) -- (p-2); \draw[line width=2,red!50] (p-6) -- (p-1); \draw[line width=2,red!50] (p-7) -- (p-1); \draw[line width=2,red!50] (p-7) -- (p-6); \draw[line width=2,red!50] (p-8) -- (p-7); \draw[line width=2,red!50] (p-8) -- (p-6); \draw[line width=2,red!50] (p-9) -- (p-7); \draw[line width=2,red!50] (p-9) -- (p-8); \draw[line width=2,red!50] (p-10) -- (p-9); \draw[line width=2,red!50] (p-11) -- (p-9); \draw[line width=2,red!50] (p-11) -- (p-10); \draw[line width=2,red!50] (p-12) -- (p-11); \draw[line width=2,red!50] (p-12) -- (p-10); \draw[line width=2,red!50] (p-13) -- (p-11); \draw[line width=2,red!50] (p-13) -- (p-12); \draw[line width=2,red!50] (p-14) -- (p-13); \draw[line width=2,red!50] (p-14) -- (p-52); \draw[line width=2,red!50] (p-15) -- (p-13); \draw[line width=2,red!50] (p-15) -- (p-14); \draw[line width=2,red!50] (p-16) -- (p-15); \draw[line width=2,red!50] (p-16) -- (p-14); \draw[line width=2,red!50] (p-17) -- (p-15); \draw[line width=2,red!50] (p-17) -- (p-16); \draw[line width=2,red!50] (p-18) -- (p-17); \draw[line width=2,red!50] (p-18) -- (p-53); \draw[line width=2,red!50] (p-19) -- (p-17); \draw[line width=2,red!50] (p-19) -- (p-18); \draw[line width=2,red!50] (p-20) -- (p-19); \draw[line width=2,red!50] (p-20) -- (p-18); \draw[line width=2,red!50] (p-21) -- (p-19); \draw[line width=2,red!50] (p-21) -- (p-20); \draw[line width=2,red!50] (p-22) -- (p-21); \draw[line width=2,red!50] (p-22) -- (p-54); \draw[line width=2,red!50] (p-23) -- (p-21); \draw[line width=2,red!50] (p-23) -- (p-22); \draw[line width=2,red!50] (p-24) -- (p-23); \draw[line width=2,red!50] (p-24) -- (p-22); \draw[line width=2,red!50] (p-25) -- (p-23); \draw[line width=2,red!50] (p-25) -- (p-24); \draw[line width=2,red!50] (p-26) -- (p-25); \draw[line width=2,red!50] (p-26) -- (p-55); \draw[line width=2,red!50] (p-27) -- (p-25); \draw[line width=2,red!50] (p-27) -- (p-26); \draw[line width=2,red!50] (p-28) -- (p-55); \draw[line width=2,red!50] (p-28) -- (p-68); \draw[line width=2,red!50] (p-28) -- (p-29); \draw[line width=2,red!50] (p-29) -- (p-27); \draw[line width=2,red!50] (p-29) -- (p-26); \draw[line width=2,red!50] (p-30) -- (p-27); \draw[line width=2,red!50] (p-30) -- (p-29); \draw[line width=2,red!50] (p-31) -- (p-30); \draw[line width=2,red!50] (p-31) -- (p-28); \draw[line width=2,red!50] (p-32) -- (p-30); \draw[line width=2,red!50] (p-32) -- (p-31); \draw[line width=2,red!50] (p-33) -- (p-32); \draw[line width=2,red!50] (p-33) -- (p-31); \draw[line width=2,red!50] (p-34) -- (p-32); \draw[line width=2,red!50] (p-34) -- (p-33); \draw[line width=2,red!50] (p-35) -- (p-34); \draw[line width=2,red!50] (p-35) -- (p-56); \draw[line width=2,red!50] (p-36) -- (p-34); \draw[line width=2,red!50] (p-36) -- (p-35); \draw[line width=2,red!50] (p-37) -- (p-36); \draw[line width=2,red!50] (p-37) -- (p-35); \draw[line width=2,red!50] (p-38) -- (p-36); \draw[line width=2,red!50] (p-38) -- (p-37); \draw[line width=2,red!50] (p-39) -- (p-38); \draw[line width=2,red!50] (p-40) -- (p-38); \draw[line width=2,red!50] (p-40) -- (p-39); \draw[line width=2,red!50] (p-41) -- (p-40); \draw[line width=2,red!50] (p-41) -- (p-39); \draw[line width=2,red!50] (p-42) -- (p-40); \draw[line width=2,red!50] (p-42) -- (p-41); \draw[line width=2,red!50] (p-42) -- (p-44); \draw[line width=2,red!50] (p-43) -- (p-44); \draw[line width=2,red!50] (p-43) -- (p-42); \draw[line width=2,red!50] (p-44) -- (p-46); \draw[line width=2,red!50] (p-45) -- (p-46); \draw[line width=2,red!50] (p-45) -- (p-43); \draw[line width=2,red!50] (p-45) -- (p-44); \draw[line width=2,red!50] (p-46) -- (p-48); \draw[line width=2,red!50] (p-47) -- (p-48); \draw[line width=2,red!50] (p-47) -- (p-46); \draw[line width=2,red!50] (p-48) -- (p-5); \draw[line width=2,red!50] (p-49) -- (p-60); \draw[line width=2,red!50] (p-49) -- (p-5); \draw[line width=2,red!50] (p-49) -- (p-47); \draw[line width=2,red!50] (p-49) -- (p-48); \draw[line width=2,red!50] (p-50) -- (p-6); \draw[line width=2,red!50] (p-50) -- (p-3); \draw[line width=2,red!50] (p-51) -- (p-10); \draw[line width=2,red!50] (p-51) -- (p-8); \draw[line width=2,red!50] (p-52) -- (p-12); \draw[line width=2,red!50] (p-52) -- (p-51); \draw[line width=2,red!50] (p-53) -- (p-16); \draw[line width=2,red!50] (p-54) -- (p-20); \draw[line width=2,red!50] (p-54) -- (p-53); \draw[line width=2,red!50] (p-55) -- (p-24); \draw[line width=2,red!50] (p-55) -- (p-61); \draw[line width=2,red!50] (p-56) -- (p-68); \draw[line width=2,red!50] (p-57) -- (p-39); \draw[line width=2,red!50] (p-57) -- (p-37); \draw[line width=2,red!50] (p-57) -- (p-58); \draw[line width=2,red!50] (p-58) -- (p-43); \draw[line width=2,red!50] (p-58) -- (p-41); \draw[line width=2,red!50] (p-58) -- (p-64); \draw[line width=2,red!50] (p-59) -- (p-47); \draw[line width=2,red!50] (p-59) -- (p-45); \draw[line width=2,red!50] (p-59) -- (p-60); \draw[line width=2,red!50] (p-60) -- (p-63); \draw[line width=2,red!50] (p-60) -- (p-4); \draw[line width=2,red!50] (p-61) -- (p-54); \draw[line width=2,red!50] (p-61) -- (p-62); \draw[line width=2,red!50] (p-62) -- (p-66); \draw[line width=2,red!50] (p-62) -- (p-65); \draw[line width=2,red!50] (p-63) -- (p-62); \draw[line width=2,red!50] (p-63) -- (p-50); \draw[line width=2,red!50] (p-64) -- (p-63); \draw[line width=2,red!50] (p-64) -- (p-59); \draw[line width=2,red!50] (p-64) -- (p-65); \draw[line width=2,red!50] (p-65) -- (p-57); \draw[line width=2,red!50] (p-66) -- (p-51); \draw[line width=2,red!50] (p-66) -- (p-50); \draw[line width=2,red!50] (p-68) -- (p-62); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ #2352 $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/3.23/4.60, 62/3.73/3.73, 63/4.60/4.23, 64/3.23/2.87, 65/4.23/4.60, 66/4.23/2.87, 67/4.60/3.23, 68/2.87/3.23, 69/2.87/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-2) -- (p-1); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-4) -- (p-3); \draw[line width=2,blue!50] (p-5) -- (p-4); \draw[line width=2,blue!50] (p-5) -- (p-2); \draw[line width=2,blue!50] (p-6) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-1); \draw[line width=2,blue!50] (p-7) -- (p-6); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-6); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-8); \draw[line width=2,blue!50] (p-10) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-9); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-12) -- (p-11); \draw[line width=2,blue!50] (p-12) -- (p-10); \draw[line width=2,blue!50] (p-13) -- (p-12); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-16) -- (p-14); \draw[line width=2,blue!50] (p-16) -- (p-53); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-18) -- (p-19); \draw[line width=2,blue!50] (p-18) -- (p-17); \draw[line width=2,blue!50] (p-19) -- (p-21); \draw[line width=2,blue!50] (p-20) -- (p-21); \draw[line width=2,blue!50] (p-20) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-19); \draw[line width=2,blue!50] (p-21) -- (p-23); \draw[line width=2,blue!50] (p-22) -- (p-23); \draw[line width=2,blue!50] (p-22) -- (p-21); \draw[line width=2,blue!50] (p-23) -- (p-25); \draw[line width=2,blue!50] (p-24) -- (p-55); \draw[line width=2,blue!50] (p-24) -- (p-22); \draw[line width=2,blue!50] (p-24) -- (p-23); \draw[line width=2,blue!50] (p-24) -- (p-25); \draw[line width=2,blue!50] (p-25) -- (p-27); \draw[line width=2,blue!50] (p-26) -- (p-25); \draw[line width=2,blue!50] (p-27) -- (p-30); \draw[line width=2,blue!50] (p-28) -- (p-65); \draw[line width=2,blue!50] (p-28) -- (p-31); \draw[line width=2,blue!50] (p-29) -- (p-28); \draw[line width=2,blue!50] (p-29) -- (p-26); \draw[line width=2,blue!50] (p-29) -- (p-30); \draw[line width=2,blue!50] (p-30) -- (p-32); \draw[line width=2,blue!50] (p-31) -- (p-32); \draw[line width=2,blue!50] (p-31) -- (p-30); \draw[line width=2,blue!50] (p-32) -- (p-34); \draw[line width=2,blue!50] (p-33) -- (p-31); \draw[line width=2,blue!50] (p-33) -- (p-32); \draw[line width=2,blue!50] (p-33) -- (p-34); \draw[line width=2,blue!50] (p-34) -- (p-36); \draw[line width=2,blue!50] (p-35) -- (p-36); \draw[line width=2,blue!50] (p-35) -- (p-34); \draw[line width=2,blue!50] (p-37) -- (p-57); \draw[line width=2,blue!50] (p-37) -- (p-35); \draw[line width=2,blue!50] (p-37) -- (p-36); \draw[line width=2,blue!50] (p-37) -- (p-38); \draw[line width=2,blue!50] (p-38) -- (p-40); \draw[line width=2,blue!50] (p-39) -- (p-38); \draw[line width=2,blue!50] (p-40) -- (p-42); \draw[line width=2,blue!50] (p-41) -- (p-58); \draw[line width=2,blue!50] (p-41) -- (p-39); \draw[line width=2,blue!50] (p-41) -- (p-42); \draw[line width=2,blue!50] (p-43) -- (p-44); \draw[line width=2,blue!50] (p-43) -- (p-42); \draw[line width=2,blue!50] (p-44) -- (p-46); \draw[line width=2,blue!50] (p-45) -- (p-43); \draw[line width=2,blue!50] (p-45) -- (p-44); \draw[line width=2,blue!50] (p-45) -- (p-46); \draw[line width=2,blue!50] (p-46) -- (p-48); \draw[line width=2,blue!50] (p-47) -- (p-48); \draw[line width=2,blue!50] (p-47) -- (p-46); \draw[line width=2,blue!50] (p-48) -- (p-5); \draw[line width=2,blue!50] (p-49) -- (p-60); \draw[line width=2,blue!50] (p-49) -- (p-5); \draw[line width=2,blue!50] (p-49) -- (p-47); \draw[line width=2,blue!50] (p-49) -- (p-48); \draw[line width=2,blue!50] (p-50) -- (p-6); \draw[line width=2,blue!50] (p-50) -- (p-3); \draw[line width=2,blue!50] (p-52) -- (p-14); \draw[line width=2,blue!50] (p-52) -- (p-12); \draw[line width=2,blue!50] (p-53) -- (p-18); \draw[line width=2,blue!50] (p-53) -- (p-52); \draw[line width=2,blue!50] (p-55) -- (p-28); \draw[line width=2,blue!50] (p-55) -- (p-26); \draw[line width=2,blue!50] (p-55) -- (p-61); \draw[line width=2,blue!50] (p-57) -- (p-58); \draw[line width=2,blue!50] (p-57) -- (p-39); \draw[line width=2,blue!50] (p-58) -- (p-43); \draw[line width=2,blue!50] (p-60) -- (p-50); \draw[line width=2,blue!50] (p-60) -- (p-4); \draw[line width=2,blue!50] (p-61) -- (p-62); \draw[line width=2,blue!50] (p-62) -- (p-64); \draw[line width=2,blue!50] (p-64) -- (p-50); \draw[line width=2,blue!50] (p-65) -- (p-61); \draw[line width=2,blue!50] (p-65) -- (p-62); \draw[line width=2,blue!50] (p-66) -- (p-62); \draw[line width=2,blue!50] (p-66) -- (p-64); \draw[line width=2,blue!50] (p-66) -- (p-60); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 15/13, 15/14, 16/15, 16/14, 16/53, 17/15, 17/16, 17/19, 18/19, 18/17, 19/21, 20/21, 20/18, 20/19, 21/23, 22/23, 22/21, 23/25, 24/55, 24/22, 24/23, 24/25, 25/27, 26/27, 26/25, 27/30, 28/65, 28/31, 29/28, 29/26, 29/27, 29/30, 30/32, 31/32, 31/30, 32/34, 33/56, 33/31, 33/32, 33/34, 34/36, 35/36, 35/34, 36/38, 37/57, 37/35, 37/36, 37/38, 38/40, 39/40, 39/38, 40/42, 41/58, 41/39, 41/40, 41/42, 42/44, 43/44, 43/42, 44/46, 45/59, 45/43, 45/44, 45/46, 46/48, 47/48, 47/46, 48/5, 49/60, 49/5, 49/47, 49/48, 50/6, 50/3, 51/10, 51/8, 52/14, 52/12, 52/68, 53/18, 53/52, 53/69, 54/22, 54/20, 54/61, 54/69, 55/28, 55/26, 55/61, 56/63, 56/35, 57/58, 57/39, 57/63, 58/67, 58/43, 59/66, 59/47, 60/50, 60/4, 61/62, 62/64, 63/62, 64/51, 64/50, 65/61, 65/62, 65/56, 66/62, 66/64, 66/60, 67/62, 67/63, 67/59, 68/51, 68/62, 69/68, 69/62} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/90, 5/330, 6/360, 7/180, 8/60, 9/180, 10/30, 11/210, 12/30, 13/240, 14/300, 15/240, 16/360, 17/120, 18/270, 19/90, 20/330, 21/90, 22/300, 23/120, 24/360, 25/60, 26/210, 27/30, 28/318, 29/270, 30/30, 31/180, 32/360, 33/300, 34/360, 35/150, 36/90, 37/270, 38/330, 39/180, 40/360, 41/180, 42/300, 43/150, 44/30, 45/150, 46/360, 47/60, 48/300, 49/120, 50/138, 51/318, 52/318, 53/138, 54/228, 55/138, 56/138, 57/138, 58/318, 59/48, 60/318, 61/150, 62/90, 63/60, 64/210, 65/30, 66/330, 67/300, 68/240, 69/120} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/3.23/4.60, 62/3.73/3.73, 63/4.60/4.23, 64/3.23/2.87, 65/4.23/4.60, 66/4.23/2.87, 67/4.60/3.23, 68/2.87/3.23, 69/2.87/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,orange!50] (p-2) -- (p-1); \draw[line width=2,orange!50] (p-3) -- (p-1); \draw[line width=2,orange!50] (p-4) -- (p-3); \draw[line width=2,orange!50] (p-5) -- (p-4); \draw[line width=2,orange!50] (p-5) -- (p-2); \draw[line width=2,orange!50] (p-6) -- (p-1); \draw[line width=2,orange!50] (p-7) -- (p-1); \draw[line width=2,orange!50] (p-7) -- (p-6); \draw[line width=2,orange!50] (p-8) -- (p-7); \draw[line width=2,orange!50] (p-8) -- (p-6); \draw[line width=2,orange!50] (p-9) -- (p-7); \draw[line width=2,orange!50] (p-9) -- (p-8); \draw[line width=2,orange!50] (p-10) -- (p-9); \draw[line width=2,orange!50] (p-11) -- (p-9); \draw[line width=2,orange!50] (p-11) -- (p-10); \draw[line width=2,orange!50] (p-12) -- (p-11); \draw[line width=2,orange!50] (p-12) -- (p-10); \draw[line width=2,orange!50] (p-13) -- (p-11); \draw[line width=2,orange!50] (p-13) -- (p-12); \draw[line width=2,orange!50] (p-14) -- (p-13); \draw[line width=2,orange!50] (p-15) -- (p-13); \draw[line width=2,orange!50] (p-16) -- (p-14); \draw[line width=2,orange!50] (p-16) -- (p-53); \draw[line width=2,orange!50] (p-17) -- (p-15); \draw[line width=2,orange!50] (p-17) -- (p-16); \draw[line width=2,orange!50] (p-17) -- (p-19); \draw[line width=2,orange!50] (p-18) -- (p-19); \draw[line width=2,orange!50] (p-18) -- (p-17); \draw[line width=2,orange!50] (p-19) -- (p-21); \draw[line width=2,orange!50] (p-20) -- (p-21); \draw[line width=2,orange!50] (p-20) -- (p-18); \draw[line width=2,orange!50] (p-20) -- (p-19); \draw[line width=2,orange!50] (p-21) -- (p-23); \draw[line width=2,orange!50] (p-22) -- (p-23); \draw[line width=2,orange!50] (p-22) -- (p-21); \draw[line width=2,orange!50] (p-23) -- (p-25); \draw[line width=2,orange!50] (p-24) -- (p-55); \draw[line width=2,orange!50] (p-24) -- (p-22); \draw[line width=2,orange!50] (p-24) -- (p-23); \draw[line width=2,orange!50] (p-24) -- (p-25); \draw[line width=2,orange!50] (p-25) -- (p-27); \draw[line width=2,orange!50] (p-26) -- (p-25); \draw[line width=2,orange!50] (p-27) -- (p-30); \draw[line width=2,orange!50] (p-28) -- (p-65); \draw[line width=2,orange!50] (p-28) -- (p-31); \draw[line width=2,orange!50] (p-29) -- (p-28); \draw[line width=2,orange!50] (p-29) -- (p-26); \draw[line width=2,orange!50] (p-29) -- (p-30); \draw[line width=2,orange!50] (p-30) -- (p-32); \draw[line width=2,orange!50] (p-31) -- (p-32); \draw[line width=2,orange!50] (p-31) -- (p-30); \draw[line width=2,orange!50] (p-32) -- (p-34); \draw[line width=2,orange!50] (p-33) -- (p-31); \draw[line width=2,orange!50] (p-33) -- (p-32); \draw[line width=2,orange!50] (p-33) -- (p-34); \draw[line width=2,orange!50] (p-34) -- (p-36); \draw[line width=2,orange!50] (p-35) -- (p-36); \draw[line width=2,orange!50] (p-35) -- (p-34); \draw[line width=2,orange!50] (p-36) -- (p-38); \draw[line width=2,orange!50] (p-37) -- (p-57); \draw[line width=2,orange!50] (p-37) -- (p-35); \draw[line width=2,orange!50] (p-37) -- (p-36); \draw[line width=2,orange!50] (p-37) -- (p-38); \draw[line width=2,orange!50] (p-38) -- (p-40); \draw[line width=2,orange!50] (p-39) -- (p-38); \draw[line width=2,orange!50] (p-40) -- (p-42); \draw[line width=2,orange!50] (p-41) -- (p-58); \draw[line width=2,orange!50] (p-41) -- (p-39); \draw[line width=2,orange!50] (p-41) -- (p-42); \draw[line width=2,orange!50] (p-42) -- (p-44); \draw[line width=2,orange!50] (p-43) -- (p-44); \draw[line width=2,orange!50] (p-43) -- (p-42); \draw[line width=2,orange!50] (p-44) -- (p-46); \draw[line width=2,orange!50] (p-45) -- (p-59); \draw[line width=2,orange!50] (p-45) -- (p-43); \draw[line width=2,orange!50] (p-45) -- (p-44); \draw[line width=2,orange!50] (p-45) -- (p-46); \draw[line width=2,orange!50] (p-46) -- (p-48); \draw[line width=2,orange!50] (p-47) -- (p-48); \draw[line width=2,orange!50] (p-47) -- (p-46); \draw[line width=2,orange!50] (p-48) -- (p-5); \draw[line width=2,orange!50] (p-49) -- (p-60); \draw[line width=2,orange!50] (p-49) -- (p-5); \draw[line width=2,orange!50] (p-49) -- (p-47); \draw[line width=2,orange!50] (p-49) -- (p-48); \draw[line width=2,orange!50] (p-50) -- (p-6); \draw[line width=2,orange!50] (p-50) -- (p-3); \draw[line width=2,orange!50] (p-51) -- (p-10); \draw[line width=2,orange!50] (p-52) -- (p-14); \draw[line width=2,orange!50] (p-52) -- (p-12); \draw[line width=2,orange!50] (p-53) -- (p-18); \draw[line width=2,orange!50] (p-53) -- (p-52); \draw[line width=2,orange!50] (p-54) -- (p-20); \draw[line width=2,orange!50] (p-54) -- (p-61); \draw[line width=2,orange!50] (p-55) -- (p-28); \draw[line width=2,orange!50] (p-55) -- (p-26); \draw[line width=2,orange!50] (p-55) -- (p-61); \draw[line width=2,orange!50] (p-56) -- (p-35); \draw[line width=2,orange!50] (p-57) -- (p-58); \draw[line width=2,orange!50] (p-57) -- (p-39); \draw[line width=2,orange!50] (p-58) -- (p-43); \draw[line width=2,orange!50] (p-59) -- (p-66); \draw[line width=2,orange!50] (p-60) -- (p-50); \draw[line width=2,orange!50] (p-60) -- (p-4); \draw[line width=2,orange!50] (p-61) -- (p-62); \draw[line width=2,orange!50] (p-62) -- (p-64); \draw[line width=2,orange!50] (p-64) -- (p-51); \draw[line width=2,orange!50] (p-64) -- (p-50); \draw[line width=2,orange!50] (p-65) -- (p-62); \draw[line width=2,orange!50] (p-65) -- (p-56); \draw[line width=2,orange!50] (p-66) -- (p-62); \draw[line width=2,orange!50] (p-66) -- (p-60); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/3.23/4.60, 62/3.73/3.73, 63/4.60/4.23, 64/3.23/2.87, 65/4.23/4.60, 66/4.23/2.87, 67/4.60/3.23, 68/2.87/3.23, 69/2.87/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,green!50] (p-2) -- (p-1); \draw[line width=2,green!50] (p-3) -- (p-2); \draw[line width=2,green!50] (p-4) -- (p-3); \draw[line width=2,green!50] (p-4) -- (p-2); \draw[line width=2,green!50] (p-5) -- (p-4); \draw[line width=2,green!50] (p-5) -- (p-2); \draw[line width=2,green!50] (p-6) -- (p-1); \draw[line width=2,green!50] (p-7) -- (p-1); \draw[line width=2,green!50] (p-7) -- (p-6); \draw[line width=2,green!50] (p-8) -- (p-7); \draw[line width=2,green!50] (p-8) -- (p-6); \draw[line width=2,green!50] (p-9) -- (p-7); \draw[line width=2,green!50] (p-9) -- (p-8); \draw[line width=2,green!50] (p-10) -- (p-9); \draw[line width=2,green!50] (p-11) -- (p-9); \draw[line width=2,green!50] (p-11) -- (p-10); \draw[line width=2,green!50] (p-12) -- (p-11); \draw[line width=2,green!50] (p-12) -- (p-10); \draw[line width=2,green!50] (p-13) -- (p-11); \draw[line width=2,green!50] (p-13) -- (p-12); \draw[line width=2,green!50] (p-14) -- (p-13); \draw[line width=2,green!50] (p-15) -- (p-13); \draw[line width=2,green!50] (p-16) -- (p-14); \draw[line width=2,green!50] (p-16) -- (p-53); \draw[line width=2,green!50] (p-17) -- (p-15); \draw[line width=2,green!50] (p-17) -- (p-16); \draw[line width=2,green!50] (p-17) -- (p-19); \draw[line width=2,green!50] (p-18) -- (p-19); \draw[line width=2,green!50] (p-18) -- (p-17); \draw[line width=2,green!50] (p-19) -- (p-21); \draw[line width=2,green!50] (p-20) -- (p-21); \draw[line width=2,green!50] (p-20) -- (p-18); \draw[line width=2,green!50] (p-20) -- (p-19); \draw[line width=2,green!50] (p-21) -- (p-23); \draw[line width=2,green!50] (p-22) -- (p-23); \draw[line width=2,green!50] (p-22) -- (p-21); \draw[line width=2,green!50] (p-23) -- (p-25); \draw[line width=2,green!50] (p-24) -- (p-55); \draw[line width=2,green!50] (p-24) -- (p-22); \draw[line width=2,green!50] (p-24) -- (p-23); \draw[line width=2,green!50] (p-24) -- (p-25); \draw[line width=2,green!50] (p-25) -- (p-27); \draw[line width=2,green!50] (p-26) -- (p-27); \draw[line width=2,green!50] (p-27) -- (p-30); \draw[line width=2,green!50] (p-28) -- (p-31); \draw[line width=2,green!50] (p-29) -- (p-28); \draw[line width=2,green!50] (p-29) -- (p-26); \draw[line width=2,green!50] (p-29) -- (p-27); \draw[line width=2,green!50] (p-29) -- (p-30); \draw[line width=2,green!50] (p-30) -- (p-32); \draw[line width=2,green!50] (p-31) -- (p-32); \draw[line width=2,green!50] (p-31) -- (p-30); \draw[line width=2,green!50] (p-32) -- (p-34); \draw[line width=2,green!50] (p-33) -- (p-56); \draw[line width=2,green!50] (p-33) -- (p-31); \draw[line width=2,green!50] (p-33) -- (p-32); \draw[line width=2,green!50] (p-33) -- (p-34); \draw[line width=2,green!50] (p-34) -- (p-36); \draw[line width=2,green!50] (p-35) -- (p-36); \draw[line width=2,green!50] (p-35) -- (p-34); \draw[line width=2,green!50] (p-37) -- (p-57); \draw[line width=2,green!50] (p-37) -- (p-35); \draw[line width=2,green!50] (p-37) -- (p-36); \draw[line width=2,green!50] (p-37) -- (p-38); \draw[line width=2,green!50] (p-38) -- (p-40); \draw[line width=2,green!50] (p-39) -- (p-38); \draw[line width=2,green!50] (p-40) -- (p-42); \draw[line width=2,green!50] (p-41) -- (p-58); \draw[line width=2,green!50] (p-41) -- (p-39); \draw[line width=2,green!50] (p-41) -- (p-42); \draw[line width=2,green!50] (p-43) -- (p-44); \draw[line width=2,green!50] (p-43) -- (p-42); \draw[line width=2,green!50] (p-44) -- (p-46); \draw[line width=2,green!50] (p-45) -- (p-43); \draw[line width=2,green!50] (p-45) -- (p-44); \draw[line width=2,green!50] (p-45) -- (p-46); \draw[line width=2,green!50] (p-46) -- (p-48); \draw[line width=2,green!50] (p-47) -- (p-48); \draw[line width=2,green!50] (p-47) -- (p-46); \draw[line width=2,green!50] (p-48) -- (p-5); \draw[line width=2,green!50] (p-49) -- (p-60); \draw[line width=2,green!50] (p-49) -- (p-5); \draw[line width=2,green!50] (p-49) -- (p-47); \draw[line width=2,green!50] (p-49) -- (p-48); \draw[line width=2,green!50] (p-50) -- (p-6); \draw[line width=2,green!50] (p-50) -- (p-3); \draw[line width=2,green!50] (p-51) -- (p-10); \draw[line width=2,green!50] (p-52) -- (p-14); \draw[line width=2,green!50] (p-52) -- (p-12); \draw[line width=2,green!50] (p-53) -- (p-18); \draw[line width=2,green!50] (p-53) -- (p-52); \draw[line width=2,green!50] (p-54) -- (p-20); \draw[line width=2,green!50] (p-54) -- (p-61); \draw[line width=2,green!50] (p-55) -- (p-28); \draw[line width=2,green!50] (p-55) -- (p-26); \draw[line width=2,green!50] (p-55) -- (p-61); \draw[line width=2,green!50] (p-56) -- (p-63); \draw[line width=2,green!50] (p-57) -- (p-58); \draw[line width=2,green!50] (p-57) -- (p-39); \draw[line width=2,green!50] (p-58) -- (p-43); \draw[line width=2,green!50] (p-59) -- (p-47); \draw[line width=2,green!50] (p-60) -- (p-50); \draw[line width=2,green!50] (p-60) -- (p-4); \draw[line width=2,green!50] (p-61) -- (p-62); \draw[line width=2,green!50] (p-62) -- (p-64); \draw[line width=2,green!50] (p-63) -- (p-62); \draw[line width=2,green!50] (p-64) -- (p-51); \draw[line width=2,green!50] (p-64) -- (p-50); \draw[line width=2,green!50] (p-67) -- (p-62); \draw[line width=2,green!50] (p-67) -- (p-63); \draw[line width=2,green!50] (p-67) -- (p-59); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/3.23/4.60, 62/3.73/3.73, 63/4.60/4.23, 64/3.23/2.87, 65/4.23/4.60, 66/4.23/2.87, 67/4.60/3.23, 68/2.87/3.23, 69/2.87/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,darkgray!50] (p-2) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-1); \draw[line width=2,darkgray!50] (p-3) -- (p-2); \draw[line width=2,darkgray!50] (p-4) -- (p-3); \draw[line width=2,darkgray!50] (p-4) -- (p-2); \draw[line width=2,darkgray!50] (p-5) -- (p-4); \draw[line width=2,darkgray!50] (p-5) -- (p-2); \draw[line width=2,darkgray!50] (p-6) -- (p-1); \draw[line width=2,darkgray!50] (p-7) -- (p-1); \draw[line width=2,darkgray!50] (p-7) -- (p-6); \draw[line width=2,darkgray!50] (p-8) -- (p-7); \draw[line width=2,darkgray!50] (p-8) -- (p-6); \draw[line width=2,darkgray!50] (p-9) -- (p-7); \draw[line width=2,darkgray!50] (p-9) -- (p-8); \draw[line width=2,darkgray!50] (p-10) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-9); \draw[line width=2,darkgray!50] (p-11) -- (p-10); \draw[line width=2,darkgray!50] (p-12) -- (p-11); \draw[line width=2,darkgray!50] (p-12) -- (p-10); \draw[line width=2,darkgray!50] (p-13) -- (p-11); \draw[line width=2,darkgray!50] (p-13) -- (p-12); \draw[line width=2,darkgray!50] (p-14) -- (p-13); \draw[line width=2,darkgray!50] (p-15) -- (p-13); \draw[line width=2,darkgray!50] (p-15) -- (p-14); \draw[line width=2,darkgray!50] (p-16) -- (p-15); \draw[line width=2,darkgray!50] (p-16) -- (p-14); \draw[line width=2,darkgray!50] (p-16) -- (p-53); \draw[line width=2,darkgray!50] (p-17) -- (p-15); \draw[line width=2,darkgray!50] (p-17) -- (p-16); \draw[line width=2,darkgray!50] (p-17) -- (p-19); \draw[line width=2,darkgray!50] (p-18) -- (p-19); \draw[line width=2,darkgray!50] (p-18) -- (p-17); \draw[line width=2,darkgray!50] (p-19) -- (p-21); \draw[line width=2,darkgray!50] (p-20) -- (p-21); \draw[line width=2,darkgray!50] (p-20) -- (p-18); \draw[line width=2,darkgray!50] (p-20) -- (p-19); \draw[line width=2,darkgray!50] (p-21) -- (p-23); \draw[line width=2,darkgray!50] (p-22) -- (p-23); \draw[line width=2,darkgray!50] (p-22) -- (p-21); \draw[line width=2,darkgray!50] (p-23) -- (p-25); \draw[line width=2,darkgray!50] (p-24) -- (p-55); \draw[line width=2,darkgray!50] (p-24) -- (p-22); \draw[line width=2,darkgray!50] (p-24) -- (p-23); \draw[line width=2,darkgray!50] (p-24) -- (p-25); \draw[line width=2,darkgray!50] (p-25) -- (p-27); \draw[line width=2,darkgray!50] (p-26) -- (p-27); \draw[line width=2,darkgray!50] (p-26) -- (p-25); \draw[line width=2,darkgray!50] (p-27) -- (p-30); \draw[line width=2,darkgray!50] (p-28) -- (p-65); \draw[line width=2,darkgray!50] (p-28) -- (p-31); \draw[line width=2,darkgray!50] (p-29) -- (p-28); \draw[line width=2,darkgray!50] (p-29) -- (p-26); \draw[line width=2,darkgray!50] (p-29) -- (p-27); \draw[line width=2,darkgray!50] (p-29) -- (p-30); \draw[line width=2,darkgray!50] (p-30) -- (p-32); \draw[line width=2,darkgray!50] (p-31) -- (p-32); \draw[line width=2,darkgray!50] (p-31) -- (p-30); \draw[line width=2,darkgray!50] (p-32) -- (p-34); \draw[line width=2,darkgray!50] (p-33) -- (p-56); \draw[line width=2,darkgray!50] (p-33) -- (p-31); \draw[line width=2,darkgray!50] (p-33) -- (p-32); \draw[line width=2,darkgray!50] (p-33) -- (p-34); \draw[line width=2,darkgray!50] (p-34) -- (p-36); \draw[line width=2,darkgray!50] (p-35) -- (p-36); \draw[line width=2,darkgray!50] (p-35) -- (p-34); \draw[line width=2,darkgray!50] (p-36) -- (p-38); \draw[line width=2,darkgray!50] (p-37) -- (p-57); \draw[line width=2,darkgray!50] (p-37) -- (p-35); \draw[line width=2,darkgray!50] (p-37) -- (p-36); \draw[line width=2,darkgray!50] (p-37) -- (p-38); \draw[line width=2,darkgray!50] (p-38) -- (p-40); \draw[line width=2,darkgray!50] (p-39) -- (p-40); \draw[line width=2,darkgray!50] (p-39) -- (p-38); \draw[line width=2,darkgray!50] (p-40) -- (p-42); \draw[line width=2,darkgray!50] (p-41) -- (p-58); \draw[line width=2,darkgray!50] (p-41) -- (p-39); \draw[line width=2,darkgray!50] (p-41) -- (p-40); \draw[line width=2,darkgray!50] (p-41) -- (p-42); \draw[line width=2,darkgray!50] (p-42) -- (p-44); \draw[line width=2,darkgray!50] (p-43) -- (p-44); \draw[line width=2,darkgray!50] (p-43) -- (p-42); \draw[line width=2,darkgray!50] (p-44) -- (p-46); \draw[line width=2,darkgray!50] (p-45) -- (p-59); \draw[line width=2,darkgray!50] (p-45) -- (p-43); \draw[line width=2,darkgray!50] (p-45) -- (p-44); \draw[line width=2,darkgray!50] (p-45) -- (p-46); \draw[line width=2,darkgray!50] (p-46) -- (p-48); \draw[line width=2,darkgray!50] (p-47) -- (p-48); \draw[line width=2,darkgray!50] (p-47) -- (p-46); \draw[line width=2,darkgray!50] (p-48) -- (p-5); \draw[line width=2,darkgray!50] (p-49) -- (p-60); \draw[line width=2,darkgray!50] (p-49) -- (p-5); \draw[line width=2,darkgray!50] (p-49) -- (p-47); \draw[line width=2,darkgray!50] (p-49) -- (p-48); \draw[line width=2,darkgray!50] (p-50) -- (p-6); \draw[line width=2,darkgray!50] (p-50) -- (p-3); \draw[line width=2,darkgray!50] (p-51) -- (p-10); \draw[line width=2,darkgray!50] (p-51) -- (p-8); \draw[line width=2,darkgray!50] (p-52) -- (p-14); \draw[line width=2,darkgray!50] (p-52) -- (p-12); \draw[line width=2,darkgray!50] (p-52) -- (p-68); \draw[line width=2,darkgray!50] (p-53) -- (p-18); \draw[line width=2,darkgray!50] (p-53) -- (p-52); \draw[line width=2,darkgray!50] (p-54) -- (p-20); \draw[line width=2,darkgray!50] (p-54) -- (p-61); \draw[line width=2,darkgray!50] (p-55) -- (p-28); \draw[line width=2,darkgray!50] (p-55) -- (p-26); \draw[line width=2,darkgray!50] (p-55) -- (p-61); \draw[line width=2,darkgray!50] (p-56) -- (p-63); \draw[line width=2,darkgray!50] (p-57) -- (p-58); \draw[line width=2,darkgray!50] (p-57) -- (p-39); \draw[line width=2,darkgray!50] (p-58) -- (p-67); \draw[line width=2,darkgray!50] (p-58) -- (p-43); \draw[line width=2,darkgray!50] (p-59) -- (p-66); \draw[line width=2,darkgray!50] (p-60) -- (p-50); \draw[line width=2,darkgray!50] (p-60) -- (p-4); \draw[line width=2,darkgray!50] (p-61) -- (p-62); \draw[line width=2,darkgray!50] (p-62) -- (p-64); \draw[line width=2,darkgray!50] (p-63) -- (p-62); \draw[line width=2,darkgray!50] (p-64) -- (p-51); \draw[line width=2,darkgray!50] (p-64) -- (p-50); \draw[line width=2,darkgray!50] (p-65) -- (p-61); \draw[line width=2,darkgray!50] (p-65) -- (p-62); \draw[line width=2,darkgray!50] (p-66) -- (p-62); \draw[line width=2,darkgray!50] (p-66) -- (p-60); \draw[line width=2,darkgray!50] (p-67) -- (p-62); \draw[line width=2,darkgray!50] (p-67) -- (p-63); \draw[line width=2,darkgray!50] (p-68) -- (p-51); \draw[line width=2,darkgray!50] (p-68) -- (p-62); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/3.23/4.60, 62/3.73/3.73, 63/4.60/4.23, 64/3.23/2.87, 65/4.23/4.60, 66/4.23/2.87, 67/4.60/3.23, 68/2.87/3.23, 69/2.87/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,red!50] (p-2) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-1); \draw[line width=2,red!50] (p-3) -- (p-2); \draw[line width=2,red!50] (p-4) -- (p-3); \draw[line width=2,red!50] (p-4) -- (p-2); \draw[line width=2,red!50] (p-5) -- (p-4); \draw[line width=2,red!50] (p-5) -- (p-2); \draw[line width=2,red!50] (p-6) -- (p-1); \draw[line width=2,red!50] (p-7) -- (p-1); \draw[line width=2,red!50] (p-7) -- (p-6); \draw[line width=2,red!50] (p-8) -- (p-7); \draw[line width=2,red!50] (p-8) -- (p-6); \draw[line width=2,red!50] (p-9) -- (p-7); \draw[line width=2,red!50] (p-9) -- (p-8); \draw[line width=2,red!50] (p-10) -- (p-9); \draw[line width=2,red!50] (p-11) -- (p-9); \draw[line width=2,red!50] (p-11) -- (p-10); \draw[line width=2,red!50] (p-12) -- (p-11); \draw[line width=2,red!50] (p-12) -- (p-10); \draw[line width=2,red!50] (p-13) -- (p-11); \draw[line width=2,red!50] (p-13) -- (p-12); \draw[line width=2,red!50] (p-14) -- (p-13); \draw[line width=2,red!50] (p-15) -- (p-13); \draw[line width=2,red!50] (p-16) -- (p-14); \draw[line width=2,red!50] (p-16) -- (p-53); \draw[line width=2,red!50] (p-17) -- (p-15); \draw[line width=2,red!50] (p-17) -- (p-16); \draw[line width=2,red!50] (p-17) -- (p-19); \draw[line width=2,red!50] (p-18) -- (p-19); \draw[line width=2,red!50] (p-18) -- (p-17); \draw[line width=2,red!50] (p-19) -- (p-21); \draw[line width=2,red!50] (p-20) -- (p-21); \draw[line width=2,red!50] (p-20) -- (p-18); \draw[line width=2,red!50] (p-20) -- (p-19); \draw[line width=2,red!50] (p-21) -- (p-23); \draw[line width=2,red!50] (p-22) -- (p-23); \draw[line width=2,red!50] (p-22) -- (p-21); \draw[line width=2,red!50] (p-23) -- (p-25); \draw[line width=2,red!50] (p-24) -- (p-55); \draw[line width=2,red!50] (p-24) -- (p-22); \draw[line width=2,red!50] (p-24) -- (p-23); \draw[line width=2,red!50] (p-24) -- (p-25); \draw[line width=2,red!50] (p-25) -- (p-27); \draw[line width=2,red!50] (p-26) -- (p-27); \draw[line width=2,red!50] (p-26) -- (p-25); \draw[line width=2,red!50] (p-27) -- (p-30); \draw[line width=2,red!50] (p-28) -- (p-31); \draw[line width=2,red!50] (p-29) -- (p-28); \draw[line width=2,red!50] (p-29) -- (p-26); \draw[line width=2,red!50] (p-29) -- (p-27); \draw[line width=2,red!50] (p-29) -- (p-30); \draw[line width=2,red!50] (p-30) -- (p-32); \draw[line width=2,red!50] (p-31) -- (p-32); \draw[line width=2,red!50] (p-31) -- (p-30); \draw[line width=2,red!50] (p-32) -- (p-34); \draw[line width=2,red!50] (p-33) -- (p-31); \draw[line width=2,red!50] (p-33) -- (p-32); \draw[line width=2,red!50] (p-33) -- (p-34); \draw[line width=2,red!50] (p-34) -- (p-36); \draw[line width=2,red!50] (p-35) -- (p-36); \draw[line width=2,red!50] (p-35) -- (p-34); \draw[line width=2,red!50] (p-36) -- (p-38); \draw[line width=2,red!50] (p-37) -- (p-57); \draw[line width=2,red!50] (p-37) -- (p-35); \draw[line width=2,red!50] (p-37) -- (p-36); \draw[line width=2,red!50] (p-37) -- (p-38); \draw[line width=2,red!50] (p-38) -- (p-40); \draw[line width=2,red!50] (p-39) -- (p-38); \draw[line width=2,red!50] (p-40) -- (p-42); \draw[line width=2,red!50] (p-41) -- (p-58); \draw[line width=2,red!50] (p-41) -- (p-39); \draw[line width=2,red!50] (p-41) -- (p-42); \draw[line width=2,red!50] (p-42) -- (p-44); \draw[line width=2,red!50] (p-43) -- (p-44); \draw[line width=2,red!50] (p-43) -- (p-42); \draw[line width=2,red!50] (p-44) -- (p-46); \draw[line width=2,red!50] (p-45) -- (p-43); \draw[line width=2,red!50] (p-45) -- (p-44); \draw[line width=2,red!50] (p-45) -- (p-46); \draw[line width=2,red!50] (p-46) -- (p-48); \draw[line width=2,red!50] (p-47) -- (p-48); \draw[line width=2,red!50] (p-47) -- (p-46); \draw[line width=2,red!50] (p-48) -- (p-5); \draw[line width=2,red!50] (p-49) -- (p-60); \draw[line width=2,red!50] (p-49) -- (p-5); \draw[line width=2,red!50] (p-49) -- (p-47); \draw[line width=2,red!50] (p-49) -- (p-48); \draw[line width=2,red!50] (p-50) -- (p-6); \draw[line width=2,red!50] (p-50) -- (p-3); \draw[line width=2,red!50] (p-51) -- (p-10); \draw[line width=2,red!50] (p-51) -- (p-8); \draw[line width=2,red!50] (p-52) -- (p-14); \draw[line width=2,red!50] (p-52) -- (p-12); \draw[line width=2,red!50] (p-52) -- (p-68); \draw[line width=2,red!50] (p-53) -- (p-18); \draw[line width=2,red!50] (p-53) -- (p-52); \draw[line width=2,red!50] (p-53) -- (p-69); \draw[line width=2,red!50] (p-54) -- (p-22); \draw[line width=2,red!50] (p-54) -- (p-20); \draw[line width=2,red!50] (p-54) -- (p-61); \draw[line width=2,red!50] (p-54) -- (p-69); \draw[line width=2,red!50] (p-55) -- (p-28); \draw[line width=2,red!50] (p-55) -- (p-26); \draw[line width=2,red!50] (p-55) -- (p-61); \draw[line width=2,red!50] (p-57) -- (p-58); \draw[line width=2,red!50] (p-57) -- (p-39); \draw[line width=2,red!50] (p-57) -- (p-63); \draw[line width=2,red!50] (p-58) -- (p-67); \draw[line width=2,red!50] (p-58) -- (p-43); \draw[line width=2,red!50] (p-60) -- (p-50); \draw[line width=2,red!50] (p-60) -- (p-4); \draw[line width=2,red!50] (p-61) -- (p-62); \draw[line width=2,red!50] (p-62) -- (p-64); \draw[line width=2,red!50] (p-63) -- (p-62); \draw[line width=2,red!50] (p-64) -- (p-51); \draw[line width=2,red!50] (p-64) -- (p-50); \draw[line width=2,red!50] (p-67) -- (p-62); \draw[line width=2,red!50] (p-67) -- (p-63); \draw[line width=2,red!50] (p-68) -- (p-51); \draw[line width=2,red!50] (p-69) -- (p-68); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ $ \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/1.87/0.50, 8/1.87/1.50, 9/1.00/1.00, 10/1.50/1.87, 11/0.50/1.87, 12/1.00/2.73, 13/0.00/2.73, 14/0.87/3.23, 15/0.00/3.73, 16/0.87/4.23, 17/0.00/4.73, 18/1.00/4.73, 19/0.50/5.60, 20/1.50/5.60, 21/1.00/6.46, 22/1.87/5.96, 23/1.87/6.96, 24/2.73/6.46, 25/2.73/7.46, 26/3.23/6.60, 27/3.73/7.46, 28/4.23/5.60, 29/4.23/6.60, 30/4.73/7.46, 31/4.73/6.46, 32/5.60/6.96, 33/5.60/5.96, 34/6.46/6.46, 35/5.96/5.60, 36/6.96/5.60, 37/6.46/4.73, 38/7.46/4.73, 39/6.60/4.23, 40/7.46/3.73, 41/6.60/3.23, 42/7.46/2.73, 43/6.46/2.73, 44/6.96/1.87, 45/5.96/1.87, 46/6.46/1.00, 47/5.60/1.50, 48/5.60/0.50, 49/4.73/1.00, 50/3.23/1.87, 51/2.37/2.37, 52/1.87/3.23, 53/1.87/4.23, 54/2.37/5.10, 55/3.23/5.60, 56/5.10/5.10, 57/5.60/4.23, 58/5.60/3.23, 59/5.10/2.37, 60/4.23/1.87, 61/3.23/4.60, 62/3.73/3.73, 63/4.60/4.23, 64/3.23/2.87, 65/4.23/4.60, 66/4.23/2.87, 67/4.60/3.23, 68/2.87/3.23, 69/2.87/4.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,violet!50] (p-2) -- (p-1); \draw[line width=2,violet!50] (p-3) -- (p-1); \draw[line width=2,violet!50] (p-4) -- (p-3); \draw[line width=2,violet!50] (p-5) -- (p-4); \draw[line width=2,violet!50] (p-5) -- (p-2); \draw[line width=2,violet!50] (p-6) -- (p-1); \draw[line width=2,violet!50] (p-7) -- (p-1); \draw[line width=2,violet!50] (p-7) -- (p-6); \draw[line width=2,violet!50] (p-8) -- (p-7); \draw[line width=2,violet!50] (p-8) -- (p-6); \draw[line width=2,violet!50] (p-9) -- (p-7); \draw[line width=2,violet!50] (p-9) -- (p-8); \draw[line width=2,violet!50] (p-10) -- (p-9); \draw[line width=2,violet!50] (p-11) -- (p-9); \draw[line width=2,violet!50] (p-11) -- (p-10); \draw[line width=2,violet!50] (p-12) -- (p-11); \draw[line width=2,violet!50] (p-12) -- (p-10); \draw[line width=2,violet!50] (p-13) -- (p-11); \draw[line width=2,violet!50] (p-13) -- (p-12); \draw[line width=2,violet!50] (p-14) -- (p-13); \draw[line width=2,violet!50] (p-15) -- (p-13); \draw[line width=2,violet!50] (p-15) -- (p-14); \draw[line width=2,violet!50] (p-16) -- (p-15); \draw[line width=2,violet!50] (p-16) -- (p-14); \draw[line width=2,violet!50] (p-16) -- (p-53); \draw[line width=2,violet!50] (p-17) -- (p-15); \draw[line width=2,violet!50] (p-17) -- (p-16); \draw[line width=2,violet!50] (p-17) -- (p-19); \draw[line width=2,violet!50] (p-18) -- (p-19); \draw[line width=2,violet!50] (p-18) -- (p-17); \draw[line width=2,violet!50] (p-19) -- (p-21); \draw[line width=2,violet!50] (p-20) -- (p-21); \draw[line width=2,violet!50] (p-20) -- (p-18); \draw[line width=2,violet!50] (p-20) -- (p-19); \draw[line width=2,violet!50] (p-21) -- (p-23); \draw[line width=2,violet!50] (p-22) -- (p-23); \draw[line width=2,violet!50] (p-22) -- (p-21); \draw[line width=2,violet!50] (p-23) -- (p-25); \draw[line width=2,violet!50] (p-24) -- (p-55); \draw[line width=2,violet!50] (p-24) -- (p-22); \draw[line width=2,violet!50] (p-24) -- (p-23); \draw[line width=2,violet!50] (p-24) -- (p-25); \draw[line width=2,violet!50] (p-25) -- (p-27); \draw[line width=2,violet!50] (p-26) -- (p-25); \draw[line width=2,violet!50] (p-27) -- (p-30); \draw[line width=2,violet!50] (p-28) -- (p-65); \draw[line width=2,violet!50] (p-28) -- (p-31); \draw[line width=2,violet!50] (p-29) -- (p-28); \draw[line width=2,violet!50] (p-29) -- (p-26); \draw[line width=2,violet!50] (p-29) -- (p-30); \draw[line width=2,violet!50] (p-30) -- (p-32); \draw[line width=2,violet!50] (p-31) -- (p-32); \draw[line width=2,violet!50] (p-31) -- (p-30); \draw[line width=2,violet!50] (p-32) -- (p-34); \draw[line width=2,violet!50] (p-33) -- (p-56); \draw[line width=2,violet!50] (p-33) -- (p-31); \draw[line width=2,violet!50] (p-33) -- (p-32); \draw[line width=2,violet!50] (p-33) -- (p-34); \draw[line width=2,violet!50] (p-34) -- (p-36); \draw[line width=2,violet!50] (p-35) -- (p-36); \draw[line width=2,violet!50] (p-35) -- (p-34); \draw[line width=2,violet!50] (p-36) -- (p-38); \draw[line width=2,violet!50] (p-37) -- (p-57); \draw[line width=2,violet!50] (p-37) -- (p-35); \draw[line width=2,violet!50] (p-37) -- (p-36); \draw[line width=2,violet!50] (p-37) -- (p-38); \draw[line width=2,violet!50] (p-38) -- (p-40); \draw[line width=2,violet!50] (p-39) -- (p-40); \draw[line width=2,violet!50] (p-39) -- (p-38); \draw[line width=2,violet!50] (p-40) -- (p-42); \draw[line width=2,violet!50] (p-41) -- (p-58); \draw[line width=2,violet!50] (p-41) -- (p-39); \draw[line width=2,violet!50] (p-41) -- (p-40); \draw[line width=2,violet!50] (p-41) -- (p-42); \draw[line width=2,violet!50] (p-42) -- (p-44); \draw[line width=2,violet!50] (p-43) -- (p-44); \draw[line width=2,violet!50] (p-43) -- (p-42); \draw[line width=2,violet!50] (p-44) -- (p-46); \draw[line width=2,violet!50] (p-45) -- (p-59); \draw[line width=2,violet!50] (p-45) -- (p-43); \draw[line width=2,violet!50] (p-45) -- (p-44); \draw[line width=2,violet!50] (p-45) -- (p-46); \draw[line width=2,violet!50] (p-46) -- (p-48); \draw[line width=2,violet!50] (p-47) -- (p-48); \draw[line width=2,violet!50] (p-47) -- (p-46); \draw[line width=2,violet!50] (p-48) -- (p-5); \draw[line width=2,violet!50] (p-49) -- (p-60); \draw[line width=2,violet!50] (p-49) -- (p-5); \draw[line width=2,violet!50] (p-49) -- (p-47); \draw[line width=2,violet!50] (p-49) -- (p-48); \draw[line width=2,violet!50] (p-50) -- (p-6); \draw[line width=2,violet!50] (p-50) -- (p-3); \draw[line width=2,violet!50] (p-51) -- (p-10); \draw[line width=2,violet!50] (p-52) -- (p-14); \draw[line width=2,violet!50] (p-52) -- (p-12); \draw[line width=2,violet!50] (p-53) -- (p-18); \draw[line width=2,violet!50] (p-53) -- (p-52); \draw[line width=2,violet!50] (p-53) -- (p-69); \draw[line width=2,violet!50] (p-54) -- (p-22); \draw[line width=2,violet!50] (p-54) -- (p-69); \draw[line width=2,violet!50] (p-55) -- (p-28); \draw[line width=2,violet!50] (p-55) -- (p-26); \draw[line width=2,violet!50] (p-55) -- (p-61); \draw[line width=2,violet!50] (p-56) -- (p-63); \draw[line width=2,violet!50] (p-57) -- (p-58); \draw[line width=2,violet!50] (p-57) -- (p-39); \draw[line width=2,violet!50] (p-57) -- (p-63); \draw[line width=2,violet!50] (p-58) -- (p-43); \draw[line width=2,violet!50] (p-59) -- (p-66); \draw[line width=2,violet!50] (p-60) -- (p-50); \draw[line width=2,violet!50] (p-60) -- (p-4); \draw[line width=2,violet!50] (p-61) -- (p-62); \draw[line width=2,violet!50] (p-62) -- (p-64); \draw[line width=2,violet!50] (p-63) -- (p-62); \draw[line width=2,violet!50] (p-64) -- (p-51); \draw[line width=2,violet!50] (p-64) -- (p-50); \draw[line width=2,violet!50] (p-65) -- (p-61); \draw[line width=2,violet!50] (p-65) -- (p-62); \draw[line width=2,violet!50] (p-66) -- (p-62); \draw[line width=2,violet!50] (p-66) -- (p-60); \draw[line width=2,violet!50] (p-69) -- (p-62); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \end{tikzpicture} $ Die vier Bereiche zum 120er stehen am Ende von Beitrag No.2366 Soweit das, was Button "acos(1/4)" ausgibt. Wenn ich mir jetzt einzelne Bereiche anschaue, wenn das Zustände innerer Spannungen sein sollen, so richtig überzeugt mich das selber noch nicht. Beim Doppelkite ja, aber hier??? Also ich schreib mal etliche Fragezeichen dran ? ??? ?? ????


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
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  Beitrag No.2395, eingetragen 2022-05-13

„aber hier??? Also ich schreib mal etliche Fragezeichen dran ? ??? ?? ????“ Mit Fragezeichen morsen? Wir brauchen zu jedem „?“ eine Frage, und dann finden sich auch antworten Möglicherweise überlagern sich die statischen Unbestimmtheiten der EK‘s, ? Wenn ein Holz als EK , mit einer kleinen Verlängerung, Spannung in einen Bereich von anderen Hölzern gibt dann sollte doch ein Gesetz der Wechselwirkung gelten, dieses Holz sollte auch Spannung erhalten wenn ein anderes aus seinem Bereich als EK getestet wird. Die Frage ist ob das dann alle anderen Hölzer ausschließt, in deinen farb-Bildern scheint das nicht der Fall zu sein, dort gibt es viele Hölzer die in mehreren Farben auftauchen also jeweils durchaus auch Spannung erhalten könnten von hölzern mit denen sie, im ersten Farbbild betrachtet keine bereichsverbindung hätten, also von denen sie ansich auch keine wechselwirkungsspannung erhalten sollten Kann es sein dass es bei statischer Unbestimmtheit doch rechnerisch gar nicht möglich ist den Bereich festzulegen? zB weil andere EK‘s über ihre notwendige eigene Unbestimmtheit wieder mehrere Lösungen zulassen,? Das könnte bedeuten der Gedankenansatz des EK Tests, ein Holz eine Spannung ausüben zu lassen und zu schauen in welchem Bereich die Spannung überall auftaucht, kann man nur mit der ersten Einsetzkante durchführen??? Weil bei einem zweiten nachfolgenden weiterem EK Test das System ja schon durch die erste EK Unbestimmt wurde? Und die erste EK beim Test der zweiten EK herauszunehmen dürfte ja eben viele verschiedene Bereiche für die zweite EK ergeben je nachdem welches Holz aus dem ersten Bereich entfernt wird In diese Richtung gingen meine Überlegungen die letzten Tage Zusätzlich verkompliziert wird es beim 120er durch seine Symmetrie , denn man kann ja mit fug und recht auch jedes einzelne Farbbild in 30 grad schritten drehen und spiegeln, da wäre es also nahezu immer möglich viele Hölzer in mehreren Farben dargestellt zu bekommen


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haribo
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Dabei seit: 25.10.2012
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  Beitrag No.2396, eingetragen 2022-05-13

\quoteon(2022-05-07 08:11 - StefanVogel in Beitrag No. 2366) Nein. Ich habe den Doppelkite nochmal mit Button "acos(1/4)" exakt gerechnet und erhalte folgende Einsetzkanten, hellblau markiert, 22 Stück. Diese Kanten werden auf Zug oder Druck beansprucht, wenn eine davon geringfügig seine Länge ändern wollte, und der Graph bleibt starr, wenn man eine der hellblauen Kanten entfernt. 22 Knoten, 2×Grad 2, 20×Grad 4, 0 Überschneidungen, 42 Kanten, minimal 0.99999999999999900080, maximal 1.00000000000000066613, Einsetzkanten=Beweglichkeit+1, $ %Eingabe war: % %Doppelkite mit Button "acos(1/4)" gerechnet % % %P[1]=[64.46921762354003,99.16660002755097]; P[2]=[36.10960881176999,57.30330001377544]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); A(11,12,ab(5,12,[1,12]),Bew(2)); W(); % % %Belastungsarray=[ % [ // 0 % 1.154508497187474, // 1 (P1-P9) % -0.5590169943749475, // 2 (P1-P10) % 0., // 3 (P1-P2) % -1., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % -1., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0.8090169943749475, // 12 (P6-P7) % 5.640576474687263, // 13 (P7-P8) % 1.154508497187474, // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 5.640576474687263, // 18 (P8-P11) % -0.5590169943749475, // 19 (P10-P11) % 0.5590169943749475, // 20 (P11-P14) % -5.640576474687263, // 21 (P11-P16) % 5.854101966249685, // 22 (P7-P12) % -1.118033988749895, // 23 (P6-P12) % -5.854101966249685, // 24 (P12-P17) % 1.118033988749895, // 25 (P12-P18) % 1., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0.5590169943749475, // 28 (P13-P14) % -1.154508497187474, // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % -1.154508497187474, // 33 (P15-P17) % -5.640576474687263, // 34 (P16-P17) % -0.8090169943749475, // 35 (P17-P18) % 0., // 36 (P18-P19) % 1., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 0., // 43 % 0., // 44 % ], % [ // 1 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P19) % 0., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 1., // 43 % 0., // 44 % ], % [ // 2 % 0., // 1 (P1-P9) % 0., // 2 (P1-P10) % 0., // 3 (P1-P2) % 0., // 4 (P1-P3) % 0., // 5 (P2-P3) % 0., // 6 (P3-P4) % 0., // 7 (P2-P4) % 0., // 8 (P4-P5) % 0., // 9 (P2-P5) % 0., // 10 (P3-P6) % 0., // 11 (P4-P6) % 0., // 12 (P6-P7) % 0., // 13 (P7-P8) % 0., // 14 (P7-P9) % 0., // 15 (P8-P9) % 0., // 16 (P8-P10) % 0., // 17 (P9-P10) % 0., // 18 (P8-P11) % 0., // 19 (P10-P11) % 0., // 20 (P11-P14) % 0., // 21 (P11-P16) % 0., // 22 (P7-P12) % 0., // 23 (P6-P12) % 0., // 24 (P12-P17) % 0., // 25 (P12-P18) % 0., // 26 (P13-P20) % 0., // 27 (P13-P21) % 0., // 28 (P13-P14) % 0., // 29 (P13-P15) % 0., // 30 (P14-P15) % 0., // 31 (P14-P16) % 0., // 32 (P15-P16) % 0., // 33 (P15-P17) % 0., // 34 (P16-P17) % 0., // 35 (P17-P18) % 0., // 36 (P18-P19) % 0., // 37 (P18-P20) % 0., // 38 (P19-P20) % 0., // 39 (P19-P21) % 0., // 40 (P20-P21) % 0., // 41 (P19-P22) % 0., // 42 (P21-P22) % 0., // 43 % 1., // 44 % ], % ]; %Beweglichkeiten=[ % [ // 0 % 6.190242179999751, // 1 % 1.647433977800997, // 2 % 6.190242179999751, // 3 % 2.920456216543136, // 4 % 5.087772581666517, // 5 % 2.283945097172066, // 6 % 5.087772581666517, // 7 % 3.556967335914206, // 8 % 6.190242179999751, // 9 % 4.193478455285277, // 10 % 3.985302983333286, // 11 % 2.920456216543136, // 12 % 3.644621141666594, // 13 % 1.693866838189221, // 14 % 4.260920382916595, // 15 % 0.5799723792898495, // 16 % 4.917431660833173, // 17 % 1.670650407995109, // 18 % 5.53373090208317, // 19 % 0.5567559490957368, // 20 % 4.877219624166592, // 21 % -0.5339220796095228, // 22 % 2.752704500833288, // 23 % 2.602200656857601, // 24 % 2.36446211416666, // 25 % -0.9442782386557109, // 26 % 3.620840869166627, // 27 % -0.7391001591326167, // 28 % 2.81496206249994, // 29 % 0.2463667197108722, // 30 % 4.071340817499907, // 31 % 0.4515447992339663, // 32 % 3.26546201083322, // 33 % 1.437011678077456, // 34 % 2., // 35 % 1.575545137826334, // 36 % 1., // 37 % 0.7877725689131669, // 38 % 2.18223105708333, // 39 % 0.3156334495853114, // 40 % 1.18223105708333, // 41 % -0.4721391193278555, // 42 % 0., // 43 % 0., // 44 % ], % [ // 1 % -5.190242179999748, // 1 % -1.647433977800997, // 2 % -5.190242179999748, // 3 % -2.920456216543136, // 4 % -4.087772581666518, // 5 % -2.283945097172066, // 6 % -4.087772581666518, // 7 % -3.556967335914206, // 8 % -5.190242179999748, // 9 % -4.193478455285277, // 10 % -2.985302983333286, // 11 % -2.920456216543136, // 12 % -2.644621141666595, // 13 % -1.693866838189221, // 14 % -3.260920382916594, // 15 % -0.5799723792898495, // 16 % -3.917431660833172, // 17 % -1.670650407995109, // 18 % -4.533730902083171, // 19 % -0.5567559490957368, // 20 % -3.877219624166593, // 21 % 0.5339220796095228, // 22 % -1.752704500833288, // 23 % -2.602200656857601, // 24 % -1.36446211416666, // 25 % 0.9442782386557109, // 26 % -2.620840869166626, // 27 % 0.7391001591326167, // 28 % -1.81496206249994, // 29 % -0.2463667197108722, // 30 % -3.071340817499906, // 31 % -0.4515447992339663, // 32 % -2.26546201083322, // 33 % -1.437011678077456, // 34 % -1., // 35 % -1.575545137826334, // 36 % 0., // 37 % -0.7877725689131669, // 38 % -1.18223105708333, // 39 % -0.3156334495853114, // 40 % -0.1822310570833297, // 41 % 0.4721391193278555, // 42 % 1., // 43 % 0., // 44 % ], % [ // 2 % 0., // 1 % 1., // 2 % 0., // 3 % 1., // 4 % 0., // 5 % 1., // 6 % 0., // 7 % 1., // 8 % 0., // 9 % 1., // 10 % 0., // 11 % 1., // 12 % 0., // 13 % 1., // 14 % 0., // 15 % 1., // 16 % 0., // 17 % 1., // 18 % 0., // 19 % 1., // 20 % 0., // 21 % 1., // 22 % 0., // 23 % 1., // 24 % 0., // 25 % 1., // 26 % 0., // 27 % 1., // 28 % 0., // 29 % 1., // 30 % 0., // 31 % 1., // 32 % 0., // 33 % 1., // 34 % 0., // 35 % 1., // 36 % 0., // 37 % 1., // 38 % 0., // 39 % 1., // 40 % 0., // 41 % 1., // 42 % 0., // 43 % 1., // 44 % ], % ]; %Vergleichsrichtung=[[1,0,0],[2,1,0]]; %Nenner=152; %DD=[ % [37,37], % [43,43], % [44,44], % ]; % %Beweglichkeitsgrad=0; %Einsetzkantenzahl=1; %Maxi=24; Maxj=1; MaxInvAij=5513.645886938864; //=Kante [ 12, 17 ] %gerechnet_mit_Button="acos(1/4)"; % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.24/4.27, 2/1.12/2.61, 3/3.12/2.47, 4/1.99/0.82, 5/0.00/0.96, 6/3.99/0.67, 7/5.51/1.97, 8/5.69/3.96, 9/3.88/3.12, 10/4.06/5.11, 11/5.87/5.95, 12/5.87/0.00, 13/9.50/4.27, 14/7.69/5.11, 15/7.87/3.12, 16/6.05/3.96, 17/6.23/1.97, 18/7.76/0.67, 19/9.75/0.82, 20/8.63/2.47, 21/10.63/2.61, 22/11.75/0.96} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %Einsetzkanten als \draw[line width=4] (p-1) -- (p-2); \draw[line width=2,blue!50] (p-1) -- (p-9); \draw[line width=2,blue!50] (p-1) -- (p-10); \draw[line width=2,blue!50] (p-3) -- (p-1); \draw[line width=2,blue!50] (p-6) -- (p-3); \draw[line width=2,blue!50] (p-6) -- (p-7); \draw[line width=2,blue!50] (p-8) -- (p-7); \draw[line width=2,blue!50] (p-9) -- (p-7); \draw[line width=2,blue!50] (p-11) -- (p-8); \draw[line width=2,blue!50] (p-11) -- (p-10); \draw[line width=2,blue!50] (p-11) -- (p-14); \draw[line width=2,blue!50] (p-11) -- (p-16); \draw[line width=2,blue!50] (p-12) -- (p-7); \draw[line width=2,blue!50] (p-12) -- (p-6); \draw[line width=2,blue!50] (p-12) -- (p-17); \draw[line width=2,blue!50] (p-12) -- (p-18); \draw[line width=2,blue!50] (p-13) -- (p-20); \draw[line width=2,blue!50] (p-14) -- (p-13); \draw[line width=2,blue!50] (p-15) -- (p-13); \draw[line width=2,blue!50] (p-17) -- (p-15); \draw[line width=2,blue!50] (p-17) -- (p-16); \draw[line width=2,blue!50] (p-17) -- (p-18); \draw[line width=2,blue!50] (p-20) -- (p-18); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 1/9, 1/10, 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 6/7, 8/7, 9/7, 9/8, 10/8, 10/9, 11/8, 11/10, 11/14, 11/16, 12/7, 12/6, 12/17, 12/18, 13/20, 13/21, 14/13, 15/13, 15/14, 16/14, 16/15, 17/15, 17/16, 17/18, 19/18, 20/18, 20/19, 21/19, 21/20, 22/19, 22/21} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/86, 2/86, 3/86, 4/206, 5/206, 6/190, 7/70, 8/355, 9/295, 10/175, 11/55, 12/230, 13/5, 14/5, 15/5, 16/125, 17/110, 18/214, 19/214, 20/214, 21/34, 22/334} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Alle anderen Kanten sind Anfügekanten. Dieses Ergebnis bedeutet, nicht nur allein die Flügelspitzen können entfernt werden, sondern auch Kanten wie P21-P13, P21-P19, P21-P2. Der verbleibende Restgraph behält dann die Eigenschaft, eine Einsetzkante zu enthalten. Ich versuche eine Erklärung, warum man beispielsweise Kanten P21-P13 als Anfügekante (ohne der wird der Graph beweglich) einstufen kann. Wenn man diese Kante entfernt \quoteoff die grundlagenforschung geht in die nächste runde um deine obige aussage zu verstehen hab ich es jetzt auch nochmal mit Stab2d versucht, und komme doch so leid es mir tut, wieder zu meinen alten ergebnissen, alles ausser den flügelspitzen wären dann wieder einsetzkanten (EK´s) was hab ich gemacht ?, den kite hatte ich ja schon früher mal in Stab2d eingegeben, nun hab ich die lagerbedingungen geändert um nur noch den stab S1 zu lagern, damit es passt hab ich ihn unten beweglich auf einen weiteren stab gelagert und das andere lager verschieblich ausgebildet um den doppelkite-effekt mit der EK herzustellen hab ich links-aussen nochmals einen weiteren stab (S22) eingefügt, der also alle kräfte des "doppel"-kites aufnimmt, das dürfte einwandfrei funktionieren, alle stäbe sind weiterhin mit ausreichend gelenken gegeneinander gelagert die geometrie sieht also so aus: https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-kite-statik-geo.jpg ich habe einen weg gefunden um einzelne stäbe sozusagen zu verlängern, indem ich allen eine dicke zuordnete kann ich jetzt einen einzelnen stab mit einer temperatur belasten, (in diesem beispiel S5) und dabei wird er länger, dann die normalkräfte anzeigen, zeigt auf welche stäbe es auswirkungen hat und damit scheint sich im ersten anschein deine version zu bestätigen, immer werden bestimmte andere stäbe belastet, und zwar untereinander immer im gleichen verhältniss zueinander, also immer S19 ungefähr viermal so stark wie S17, S17 ~doppelt so stark wie S10... usw https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-kite-statik-40.jpg die lastverhältnisse untereinander bleiben also in konstanten verhältnissen zueinander, auch der zweite-kite-ersatzstab "S22" wird immer belastet da ich ausser der erwärmung keine weiteren lasten ins system eingebe bleiben die beiden vorhandenen lager von Stab 1 auch weiterhin unbelastet, diese lagerung spielt also für die internen kräfte wirklich keinerlei rolle soweit bestätigen sich also deine angaben dann ist mir ein missgeschick unterlaufen, versehentlich hab ich S8 ausgewählt zum erwärmen, und das verteilungsergebniss blieb gleich! wieder wurden die gleichen stäbe als belastet angezeigt und wiederum die belastung in den gleichen verhältnissen untereinander dargestellt nach längerem suchen hab ich die darstellung der normalkräfte um den faktor 1000 erhöht und dann zeigte sich das hier diese stäbe doch auch immer mit eingebunden sind in den belastungen, aber eben nur im gaaaaaaanz geringen ausmass in dieser 1000 fach vergrösserten NORMALKRAFT darstellung erkennt man die verhältnisse von S8 zu S4;S6;S9+S12 sowie auch noch zu S16;16;18, alle anderen Normalkraft belastungen liegen weit ausserhalb des bildrands, (äh wohl soger ausserhalb der wohnung?), ja man muss sich etwas hineindenken in das strichgewirr https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-kite-statik-40T.jpg ich vermute also dass du diese geringen belastungen im nachkommabereich weg-gekürzt haben könntest? bzw es mag sich auch um klitzekleine rundungsfehler bei einem von uns beiden handeln, mir wäre aber nicht entscheidbar bei wem??? bisher hat bei mir Stab2d immer absolut rechnerisch correkt gerechnet mir ist klar dass ich damit immer nur eine EK habe, also meine fragen von heute morgen noch gar nicht bearbeiten kann


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4173
Wohnort: Raun
  Beitrag No.2397, eingetragen 2022-05-14

\quoteon(2022-05-13 07:15 - haribo in Beitrag No. 2395) Mit Fragezeichen morsen? Wir brauchen zu jedem „?“ eine Frage, und dann finden sich auch antworten \quoteoff Das ist auch eine Idee, ein unbekannter Morsecode. Ich hatte an den Ergebnissen gezweifelt und konnte es nicht in Worten ausdrücken. Der Vorteil von vielen Fragezeichen ist, es gibt dann viel zum Abhaken und das will ich sogleich tun: ✓ ✓✓✓ ✓✓ ✓✓✓✓. Die Begründung folgt. Vorher erst noch meine volle Zustimmung zu deinen weiteren Überlegungen. Zu jedem Satz ein "ja" und das zu machen ist mir die Mühe wert. \quoteon Möglicherweise überlagern sich die statischen Unbestimmtheiten der EK‘s, ? \quoteoff Ich denke ja, das kann man bei Belastungen als Idealfall annehmen. \quoteon Wenn ein Holz als EK , mit einer kleinen Verlängerung, Spannung in einen Bereich von anderen Hölzern gibt dann sollte doch ein Gesetz der Wechselwirkung gelten, dieses Holz sollte auch Spannung erhalten wenn ein anderes aus seinem Bereich als EK getestet wird. \quoteoff Sehe ich auch so. Man kann den gemessenen Spannungen nicht ansehen, welches Holz der Verursacher ist. \quoteon Die Frage ist ob das dann alle anderen Hölzer ausschließt, in deinen farb-Bildern scheint das nicht der Fall zu sein, dort gibt es viele Hölzer die in mehreren Farben auftauchen also jeweils durchaus auch Spannung erhalten könnten von hölzern mit denen sie, im ersten Farbbild betrachtet keine bereichsverbindung hätten, also von denen sie ansich auch keine wechselwirkungsspannung erhalten sollten \quoteoff Die verschiedenen Farbbilder unterscheiden sich dadurch, dass aus dem (nicht gezeichneten) Graph unterschiedliche Hölzer entfernt wurden. Dadurch ergeben sich für ein konkret betrachtetes Holz unterschiedliche Bereiche, woher und wohin Spannungen wirken. \quoteon Kann es sein dass es bei statischer Unbestimmtheit doch rechnerisch gar nicht möglich ist den Bereich festzulegen? zB weil andere EK‘s über ihre notwendige eigene Unbestimmtheit wieder mehrere Lösungen zulassen,? \quoteoff Das wollte ich mit der Bezeichnung Lösungsmenge ausdrücken, bei mehreren EK's kann man keine eindeutige Lösung angeben. Man kann dann die mit geringstem Energiegehalt nehmen, alle anderen Lösungen sind aber auch zulässig. \quoteon Das könnte bedeuten der Gedankenansatz des EK Tests, ein Holz eine Spannung ausüben zu lassen und zu schauen in welchem Bereich die Spannung überall auftaucht, kann man nur mit der ersten Einsetzkante durchführen??? Weil bei einem zweiten nachfolgenden weiterem EK Test das System ja schon durch die erste EK Unbestimmt wurde? \quoteoff Ja, nur die erste EK drinlassen und alle anderen EK herausnehmen, dann hat man wenigstens für diese Situation einen eindeutig bestimmten Bereich. \quoteon Und die erste EK beim Test der zweiten EK herauszunehmen dürfte ja eben viele verschiedene Bereiche für die zweite EK ergeben je nachdem welches Holz aus dem ersten Bereich entfernt wird \quoteoff Ja, dann nur die zweite EK einsetzen und alle anderen EK herausnehmen ergibt wieder einen eindeutig bestimmten Bereich. Dieser Bereich ist nicht nur von der einen eingesetzten EK abhängig, sondern auch von der Auswahl der anderen herausgenommenen EK's. Mit der eingesetzten EK bestimmt man, welches Holz eine Spannung erzeugen soll, mit den herausgenommenen EK's reguliert man, welche Bahn die Spannungen nehmen sollen durch den gesamten Graph hindurch. \quoteon In diese Richtung gingen meine Überlegungen die letzten Tage Zusätzlich verkompliziert wird es beim 120er durch seine Symmetrie , denn man kann ja mit fug und recht auch jedes einzelne Farbbild in 30 grad schritten drehen und spiegeln, da wäre es also nahezu immer möglich viele Hölzer in mehreren Farben dargestellt zu bekommen \quoteoff Da bin ich auch noch am Überlegen, wie man einen Überblick über die Bereiche erhalten kann. Evenuell einmal komplett alle möglichen Bereiche bestimmen und schauen, ob da markante Bereiche dabei sind und ob man die anderen daraus herleiten kann durch Überlagerungen. \quoteon(2022-05-13 14:14 - haribo in Beitrag No. 2396) um deine obige aussage zu verstehen hab ich es jetzt auch nochmal mit Stab2d versucht, und komme doch so leid es mir tut, wieder zu meinen alten ergebnissen, alles ausser den flügelspitzen wären dann wieder einsetzkanten (EK´s) \quoteoff Das Ergebnis habe ich doch auch, in Beitragh No.2366 der blau gestrichelte Graph unter dem Absatz "Im Vergleich dazu, bei exakter Berechnung mit gerundeten Punktkoordinaten (Button "GAP") liegen die Kanten P13-P20-P18 nicht unbedingt exakt auf einer Linie..." \quoteon was hab ich gemacht ?, den kite hatte ich ja schon früher mal in Stab2d eingegeben, ... ich habe einen weg gefunden um einzelne stäbe sozusagen zu verlängern, indem ich allen eine dicke zuordnete kann ich jetzt einen einzelnen stab mit einer temperatur belasten, (in diesem beispiel S5) und dabei wird er länger, dann die normalkräfte anzeigen, zeigt auf welche stäbe es auswirkungen hat und damit scheint sich im ersten anschein deine version zu bestätigen, immer werden bestimmte andere stäbe belastet, und zwar untereinander immer im gleichen verhältniss zueinander, also immer S19 ungefähr viermal so stark wie S17, S17 ~doppelt so stark wie S10... usw ... \quoteoff Perfekt, sogar mit Temperaturerhöhung, damit können wir die Ergebnisse vergleichen. Im Quellcode zum blau gestrichelten Graph (Graph wie Text markieren und in einen beliebigen Texteditor kopieren) stehen die Belastungen unter der Stelle "Belastungsarray=". Konkret für die genannten Kanten S19, S17, S10 (ich habe diese Bezeichnungen in den nächsten Zeilen rechts ergänzt) \sourceon % 7311410.868029759, // 21 (P11-P16) = S19 % 1496492.291034649, // 29 (P13-P15) = S17 % -1296215.657240261, // 26 (P13-P20) = S10 % -724607.4413395916, // 28 (P13-P14) = S20 \sourceoff Na gut, S19 knapp fünfmal so stark belastet wie S17 und S17 etwa genausoviel wie S10, dafür doppelt so stark wie S20, stimmt noch nicht so richtig überein. \quoteon dann ist mir ein missgeschick unterlaufen, versehentlich hab ich S8 ausgewählt zum erwärmen, und das verteilungsergebniss blieb gleich! wieder wurden die gleichen stäbe als belastet angezeigt und wiederum die belastung in den gleichen verhältnissen untereinander dargestellt \quoteoff Das macht Button "GAP" auch, die theoretischen Nullstäbe als EK's verwenden, in #2393 die Kanten P20-P21, P41-P42, P93-P94 und P113-P114. Ich habe da im Moment noch keine Wahlmöglichkeit drin, eine bestimmte EK zu verwenden. In #2293 ist der Quellcode nicht dabei, weil tikz so viel Eingabe nicht mehr mitmacht. Die groẞen Graphen mit den farbigen Bereichen lassen sich deshalb nicht zurückkopieren ins Streichholzprogramm. \quoteon nach längerem suchen hab ich die darstellung der normalkräfte um den faktor 1000 erhöht und dann zeigte sich das hier diese stäbe doch auch immer mit eingebunden sind in den belastungen, aber eben nur im gaaaaaaanz geringen ausmass in dieser 1000 fach vergrösserten NORMALKRAFT darstellung erkennt man die verhältnisse von S8 zu S4;S6;S9+S12 sowie auch noch zu S16;16;18, alle anderen Normalkraft belastungen liegen weit ausserhalb des bildrands, (äh wohl soger ausserhalb der wohnung?), ja man muss sich etwas hineindenken in das strichgewirr ... ich vermute also dass du diese geringen belastungen im nachkommabereich weg-gekürzt haben könntest? \quoteoff Beim #2366 habe ich die geringen Belastungen extra dringelassen, damit die gestrichelten Kanten gezeichnet werden. Ich würde sie aber gerne weglassen, wenn soweit Einverständnis besteht, solche Kanten als Nullstäbe zu betrachten. Eventuell unter der Bedingung, dass das durch zusätzliche Überlegungen begründet werden muss. \quoteon bzw es mag sich auch um klitzekleine rundungsfehler bei einem von uns beiden handeln, mir wäre aber nicht entscheidbar bei wem??? bisher hat bei mir Stab2d immer absolut rechnerisch correkt gerechnet \quoteoff Für den gedachten Anwendungsbereich des Programms sind solche geringen Restspannungen sicher korrekt, denn in der Realität wird doch eine Ausrichtung der Kanten exakt auf einer Linie kaum erreicht und auch nicht beabsichtigt. Solange diese Belastungen vernachlässigbar sind, stören sie ja nicht. \quoteon mir ist klar dass ich damit immer nur eine EK habe, also meine fragen von heute morgen noch gar nicht bearbeiten kann \quoteoff Das können wir trennen, einmal wie den Bereich bestimmen bei nur einer EK, und dann wie die Bereiche zusammenwirken bei mehreren EK.


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2398, eingetragen 2022-05-14

\quoteon(2022-05-14 07:50 - StefanVogel in Beitrag No. 2397) \quoteon Beim #2366 habe ich die geringen Belastungen extra dringelassen, damit die gestrichelten Kanten gezeichnet werden. Ich würde sie aber gerne weglassen, wenn soweit Einverständnis besteht, solche Kanten als Nullstäbe zu betrachten. Eventuell unter der Bedingung, dass das durch zusätzliche Überlegungen begründet werden muss. \quoteoff bin noch nicht ganz einverstanden, diese stäbe zu ignorieren, es betrifft ja einerseits S4; 6; 8; 9; 12; (die untereinander alle ähnliche spannungswerte haben, aber auch zusätzlich noch die anderen drei S15; 16; 18; welche gegenüber den ersten 5 auch wieder ein mehrfaches (geschätzt 5,5 faches) an spannung erhalten, diese spannungsdifferenz bedeutet doch das eine krafterhöhung (bzw andersherum absenkung) erfolgt, also dass geometrische bewegungen ausgeführt werden auch wenn sie klein sind, darum fällt es mit schwer sie alle null-stäbe werden zu lassen ich versuche gleich noch den 4/4 168 dranzu hängen, der muss ja auch drei EK´s haben, dein program wählt auch welche aus, mir scheint aber auch dort dass es nahezu alle stäbe sein können (einzig mir bekannte einschränkung, es dürfen nicht alle 3 EK von einem gemeinsamen punkt ausgehen, weil dann der vierte an diesem punkt lose wird), im streichholz-program werden aber bei vielen auswahlen dann immer beweglichkeit 3 angezeigt, die aber nie darstellbar ist, es ist also ähnlich zum 120er nur dass der 168 eben als ganzes nicht beweglich ist (darum also nur 3EK anstelle 4EK haben wird) du schriebst letztlich ich solls im hide/show bereich versuchen (was mag sich dadurch ändern?), hm klappt grad auch nicht, ick probiers noch etwas... \showon 84 Knoten, 84×Grad 4, 0 Überschneidungen, 168 Kanten, minimal 0.99999999999988475885, maximal 1.00000000000001798561, Einsetzkanten=Beweglichkeit+3, einzustellende Kanten, Abstände und Winkel: |P36-P38|=0.99999999999999078515 |P31-P30|=1.00000000000000932587 |P42-P43|=0.99999999999997624123 |P5-P46|=1.00000000000000044409 |P77-P79|=0.99999999999999300559 |P60-P61|=0.99999999999999023004 |P64-P65|=0.99999999999994482192 $ %Eingabe war: % % 4-168 % % % % % % % % % %P[1]=[91.07360855224796,-122.49946435013979]; P[2]=[147.2685250944052,-119.90641868476077]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); L(32,3,4); M(6,1,2,blauerWinkel); L(7,1,6); L(8,7,6); L(9,7,8); L(34,8,6); M(105,34,6,81.3641488633679); L(36,34,105); M(33,32,3,228.6358511366326) ; L(106,32,33); Q(35,34,32,ab(105,34,36,"gedreht"),ab(106,32,33,"gedreht")); M(10,9,7,gruenerWinkel); L(11,9,10); L(12,11,10); L(13,11,12); L(38,12,10); M(107,36,34,343.1479499200612); L(39,107,36); A(38,36,ab(107,36,39,"gedreht")); M(14,13,11,122.69518092463107); L(15,13,14); L(16,15,14); L(17,15,16); L(108,16,14); M(109,39,36,155.42347865136645) ; L(40,109,39); Q(37,13,39,ab(108,13,14,15,16,17,"gedreht"),ab(109,39,40,"gedreht")); M(18,17,15,orangerWinkel); L(19,17,18); L(20,19,18); L(21,19,20); L(31,20,18); M(30,31,18,228.6358511366326); L(110,30,31); A(40,31,ab(110,31,30,"gedreht")); M(22,21,19,122.6951809246311); L(23,21,22); L(24,23,22); L(25,23,24); L(111,24,22); M(112,30,31,215.42347865136574) ; L(42,112,30); Q(41,21,30,ab(111,21,22,23,24,25,"gedreht"),ab(112,30,42,"gedreht")); M(26,25,23,vierterWinkel); L(27,25,26); L(28,27,26); L(29,27,28); L(43,28,26); M(113,42,30,283.14794992006284); L(44,113,42); A(43,42,ab(113,42,44,"gedreht")); M(70,29,27,182.6951809246311); L(71,70,29); M(68,70,29,185); L(115,68,70); Q(69,70,71,ab(115,70,68,"gedreht"),D); L(114,69,71); M(83,44,42,95.42347865136576) ; L(116,44,83); Q(84,29,44,ab(114,29,68,69,70,71,"gedreht"),ab(116,44,83,"gedreht")); M(74,33,32,fuenfterWinkel); L(76,33,74); M(46,5,2,234.1237523532025); M(45,46,5,185.00000000000003) ; L(47,46,45); L(118,46,47); Q(48,5,46,D,ab(118,46,45,47,"gedreht")); L(117,48,47); A(74,5,ab(117,5,45,46,47,48,"gedreht")); M(119,76,33,214.57652134863508); L(77,76,119); M(49,45,46,247.3048190753694) ; L(50,49,45); L(51,49,50); L(52,51,50); L(120,49,51); Q(75,76,45,ab(119,76,77,"gedreht"),ab(120,45,49,50,51,52,"gedreht")); M(53,52,50,sechsterWinkel); L(54,53,52); L(55,53,54); L(56,55,54); L(79,53,55); M(121,77,75,26.852050079935633); L(80,77,121); A(79,77,ab(121,77,80,"gedreht")); M(122,80,77,214.57652134863474); L(81,80,122); M(57,56,54,247.3048190753689) ; L(58,57,56); L(59,57,58); L(60,59,58); L(123,57,59); Q(78,80,56,ab(122,80,81,"gedreht"),ab(123,56,57,58,59,60,"gedreht")); M(124,83,44,223.14794992006293); L(82,83,124); M(125,81,78,86.85205007993682) ; L(73,125,81); Q(72,83,81,ab(124,83,82,"gedreht"),ab(125,81,73,"gedreht")); M(61,60,58,294.12375235320275); L(62,61,60); L(63,61,62); L(64,63,62); L(126,61,63); A(73,60,ab(126,60,61,62,63,64,"gedreht")); M(65,64,62,247.3048190753688); L(66,65,64); L(67,65,66); L(127,67,66); L(82,65,67); A(68,64,ab(127,64,65,66,67,82,"gedreht")); %R(36,38); // oder R(36,39); %R(31,30); // oder R(31,40); %R(42,43); // oder R(42,44); %R(5,46); // oder R(5,48); %R(77,79); // oder R(77,80); %R(60,61); // oder R(60,62); %R(64,65); // oder R(64,66); %A(82,83); A(82,72); % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/4.57385530861825539972/0.01176870440644077302, 2/5.57279238169217006060/0.05786343337320590252, 3/5.03340463888943556725/0.89992095095390589599, 4/6.03234171196335111631/0.94601567992067103763, 5/6.57172945476608649784/0.10395816233997104416, 6/4.06876796660059891764/0.87483693863449929484, 7/3.57387262156855012307/0.00588435220322038651, 8/3.06878527955089364099/0.86895258643127859521, 9/2.57388993451884573460/0.00000000000000000000, 10/2.89593425492722289505/0.94672459337058878504, 11/1.91502454647661157772/0.75226085930344444019, 12/2.23706886688498851612/1.69898545267403311421, 13/1.25615915843437764288/1.50452171860688888039, 14/1.61601626867602732318/2.43752914634180717357, 15/0.62807957921718882144/2.28267083167607465199, 16/0.98793668945883827970/3.21567825941099316722, 17/0.00000000000000000000/3.06081994474526064565, 18/0.94097044184501577035/3.39930868543539865811, 19/0.17734537258984447994/4.04496862193838069288, 20/1.11831581443486038907/4.38345736262852003762, 21/0.35469074517968895988/5.02911729913150207238, 22/1.30851256392138992624/5.32949029740577007175, 23/0.57147100743412293511/6.00533772398282650329, 24/1.52529282617582429005/6.30571072225709539083, 25/0.78825126968855774301/6.98155814883415004601, 26/1.63957789796193176279/6.45692211119215819792, 27/1.66826272016401766507/7.45651061701604778165, 28/2.51958934843739212894/6.93187457937405770991, 29/2.54827417063947736509/7.93146308519794640546, 30/2.32937724523135303301/4.63211319942414334605, 31/1.88194088369003154071/3.73779742612553755876, 32/5.49295396916061573478/1.78807319750137105885, 33/5.21265882355691623218/2.74798706413264381965, 34/3.56368062458294199146/1.73790517286255741247, 35/4.52149660241113693360/2.02528741416674629150, 36/3.79370829193110292721/2.71108926246450154807, 37/1.97587337891767655940/3.37053657407672613289, 38/3.21797857533559961141/1.89344918674117757007, 39/2.79774635690471651372/2.80086578488816906329, 40/2.88015924314241678061/3.79746405710319301363, 41/2.26233438266309105913/5.62986329568003984747, 42/3.15993274393319811821/5.18904906967863421841, 43/2.49090452623530689280/5.93228607355016812619, 44/3.46908076146965793640/6.14006300398940574325, 45/7.80948632597483971551/1.67493172283534663691, 46/7.19060789037046266259/0.88944494258765927075, 47/6.81979560214130842155/1.81815277979926559482, 48/6.20091716653693136863/1.03266599955157789559, 49/7.40162525927441539153/2.58797572520872209978, 50/8.39627509345298861376/2.48467176899922082001, 51/7.98841402675256340160/3.39771577137259539469, 52/8.98306386093113751201/3.29441181516309500310, 53/8.02577315566952798065/3.58353895954724155359, 54/8.75480996026065660942/4.26801345691844336017, 55/7.79751925499904618988/4.55714060130258946657, 56/8.52655605959017393047/5.24161509867379127314, 57/7.55841229799311431492/5.49201010038248504941, 58/8.25933261125202200503/6.20524969158661665602, 59/7.29118884965496327766/6.45564469329531043229, 60/7.99210916291386919141/7.16888428449944026255, 61/7.16919946685351749949/6.60071209921592938485, 62/7.08860276870445371600/7.59745889366649151953, 63/6.26569307264409403047/7.02928670838297620094, 64/6.18509637449503024698/8.02603350283353833561, 65/5.38570191701769385162/7.42522696046369645728, 66/5.26508541730428270000/8.41792613946853762741, 67/4.46569095982684061141/7.81711959709874459890, 68/4.34507446011342857162/8.80981877610358665720, 69/4.27621355868639874132/7.81219250527133990403, 70/3.44667431537645452266/8.37064093065076697542, 71/3.37781341394942380418/7.37301465981852022225, 72/5.35863691217739912531/6.18919823917598943552, 73/6.34628977079315603760/6.03253991393241406627, 74/5.83010487830777712759/1.96137383676318366454, 75/6.99376419257399106755/3.50101972758209534220, 76/6.20260888878716443173/2.88940441932863567587, 77/6.06851214638963032399/3.88037266487355170241, 78/6.59026853639605558755/5.74240510209117971385, 79/7.06848245040792111382/3.87266610393138810409, 80/6.57517137595049749876/4.74251907071236278313, 81/5.71679325211001643225/5.25553661087263446205, 82/4.58630745954025176303/6.82442041809390431695, 83/4.42235364186861179547/5.83795240256025937953, 84/4.20735265725936979919/6.81456623443909226268} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/2.64/120.34/0.4/Blue, 9/0.34/71.21/0.4/Green, 17/308.91/379.78/0.4/Orange, 25/257.48/328.36/0.4/Violet, 33/286.28/308.13/0.4/Teal, 52/234.07/523.19/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/1, 7/6, 8/7, 8/6, 9/7, 9/8, 10/9, 11/9, 11/10, 12/11, 12/10, 13/11, 13/12, 14/13, 15/13, 15/14, 16/15, 16/14, 17/15, 17/16, 18/17, 19/17, 19/18, 20/19, 20/18, 21/19, 21/20, 22/21, 23/21, 23/22, 24/23, 24/22, 25/23, 25/24, 26/25, 27/25, 27/26, 28/27, 28/26, 29/27, 29/28, 30/31, 31/20, 31/18, 32/3, 32/4, 33/32, 34/8, 34/6, 35/34, 35/32, 35/33, 36/34, 36/35, 37/14, 37/16, 37/39, 38/12, 38/10, 38/36, 39/38, 39/36, 40/37, 40/39, 40/30, 40/31, 41/22, 41/24, 41/30, 42/41, 42/30, 43/28, 43/26, 43/42, 44/43, 44/42, 45/46, 46/5, 47/46, 47/45, 48/5, 48/46, 48/47, 49/45, 50/49, 50/45, 51/49, 51/50, 52/51, 52/50, 53/52, 54/53, 54/52, 55/53, 55/54, 56/55, 56/54, 57/56, 58/57, 58/56, 59/57, 59/58, 60/59, 60/58, 61/60, 62/61, 62/60, 63/61, 63/62, 64/63, 64/62, 65/64, 66/65, 66/64, 67/65, 67/66, 68/70, 68/66, 68/67, 69/68, 69/70, 69/71, 70/29, 71/70, 71/29, 72/83, 72/81, 73/72, 73/81, 73/61, 73/63, 74/33, 74/47, 74/48, 75/76, 75/49, 75/51, 76/33, 76/74, 77/76, 77/75, 78/80, 78/57, 78/59, 79/53, 79/55, 79/77, 80/77, 80/79, 81/80, 81/78, 82/65, 82/67, 82/83, 82/72, 83/44, 84/69, 84/71, 84/44, 84/83} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,84} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/2.64/120.34/0.4/Blue, 9/0.34/71.21/0.4/Green, 17/308.91/379.78/0.4/Orange, 25/257.48/328.36/0.4/Violet, 33/286.28/308.13/0.4/Teal, 52/234.07/523.19/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/330, 2/213, 3/153, 4/33, 5/262, 6/30, 7/330, 8/210, 9/210, 10/41, 11/221, 12/161, 13/279, 14/279, 15/159, 16/99, 17/159, 18/350, 19/170, 20/350, 21/110, 22/287, 23/107, 24/107, 25/178, 26/238, 27/178, 28/358, 29/176, 30/244, 31/213, 32/316, 33/76, 34/227, 35/347, 36/107, 37/175, 38/41, 39/145, 40/55, 41/124, 42/4, 43/162, 44/42, 45/264, 46/322, 47/82, 48/142, 49/264, 50/324, 51/144, 52/313, 53/253, 54/313, 55/133, 56/73, 57/195, 58/315, 59/195, 60/75, 61/305, 62/125, 63/125, 64/125, 65/247, 66/67, 67/127, 68/127, 69/296, 70/56, 71/236, 72/351, 73/21, 74/142, 75/8, 76/38, 77/128, 78/59, 79/330, 80/90, 81/261, 82/111, 83/312, 84/296} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ \showoff


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3885
  Beitrag No.2399, eingetragen 2022-05-14

\quoteon(2022-05-14 07:50 - StefanVogel in Beitrag No. 2397) Na gut, S19 knapp fünfmal so stark belastet wie S17 und S17 etwa genausoviel wie S10, dafür doppelt so stark wie S20, stimmt noch nicht so richtig überein. \quoteoff das bekommen wir genauer hin, ich kann auch irgendwo zahlen auslesen, wichtig war mir mehr die erkenntniss dass es sich immer um gleiche (oder ähnliche) verhältnisse handelt stab haribo faktor stefan faktor S19 3020 ----- 7311410 ----- S17 595 5,08 1496492 4,89 S10 -514 -1,16 -1296215 -1,15 S20 -287 1,79 -724607 1,79 S18 -13 22,08 S8 -2,4 5,42 der kleine unterschied in S19-S17 mag an meinem zweiten-kite-ersatzstab liegen... soll jetzt also egal sein und hab damit auch den faktor 22 ermittelt zwischen S20 und S18


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