! Penrose Batman CartwheelGlassSorcery.com%Penrose, geometric, Batman, cartwheelThe Batman Cartwheel - 658 pieces In some ways the pattern here, the Cartwheel, is the most important Penrose Tiling. The purple region at the center is outlined by a decagon consisting of a kite and dart edge. Every point in every tiling is contained inside an identical decagon (although the contents may differ). The outer portion of the pattern consists of two parts. There are ten yellow (here I have used gold & purple) sectors and ten blue spokes. The spokes consist of "bowtie" units and the spokes can be flipped 180 degrees and still fit their adjacent sectors. That means there are 1024 possible spoke arrangements but after rotations and reflections are eliminated there are only 62 distinct patterns. Each of the spokes can be continued inside the cartwheel, but eventually they end, enclosing a region that Penrose calls a "decapod" (in red, except for Batman darts in black.) All decapods can be constructed out of 36-108-36 isosceles triangles. The one shown here, dubbed "Batman", is the only one of the 62 decapods that can be legally tiled with darts and kites. The five darts in a Batman figure and the two intervening kites are the only tiles in any Penrose tiling that are ever part of a pattern without fivefold symmetry. http://www.uwgb.edu/dutchs/symmetry/penrose.htmPanel GeometricFreeform Vk {zBz@OLAQRRLUxL6??>yCATimes New Roman"ArialNew Roman"Verdanaw Romanث% 3/32"3.2mm1/8"4.6mm5/32"5.2mm3/16"5.9mm7/32"6.4mm1/4"7.0mm5/16"8.0mm3/8"10.0mm1/2"12.7mm1/32" (copper foil)0.8mm (copper foil)1/16" (lead came)1.6mm (lead came) R)3NcSpectrum ArmstrongWispy\3196S.jpgu,Semi-Translucent\6755S.jpgb)Waterglass\161W.jpg޵Waterglass\125W.jpg_&Translucent\3872S.jpglpoWaterglass\134W.jpglBaroque\BRCLEAR.jpgTranslucent\307S.jpgWaterglass\5432W.jpg\H|Waterglass\146W.jpgU!/Yellow\0176S.jpgdBlue\4100SO.jpgnCathedral\1009S.jpgWaterglass\1102W.jpgҢLWaterglass\1308W.jpgWaterglass\1408W.jpgWaterglass\5342W.jpg`DnWaterglass\152W.jpg$00b2b2b2Cathedral\151RR.jpg/ ~[=> >@>`>>>>?.>r9>FQ>m>>4>B>&>~=~[==.==fϔAh@l?\ǢA( @_R?A.AxXb?MAڹAIk?HBAMHAݔ?(AmA^|?zA*&TAZ?|A`A>~nAPD@\o?RA%A ?/AB~A[?YAA?O'AәAK`?/GA $HAj?o7A9A۾\?qe>A`8A ?A׫AG3 ?A(Aq ?KoSAARD?nA̓A^c?<AA?GiAmAc?aUA@v?%ԼA1Af?sAoA\>}ASDAy? ArDAY?{maAAft?߆A@ ?lpAf{A2 ?v7XAC›A`?jAsASh?(R5AeIAs>W2AA|?NXA2@w?#jA&A p?=AދA>dA^4A>ōARi@%l?\}A~AI_?M]bAA? 0A˓A?>A{.AQ?D'AAW[?&!AAR?AA(?Z ADGA<>ASHAI?RA*A_?NA]A:o?EA7A[ ?ֱAhVANAA5A> A AA[nApPAq{ACDA4aAc@wA@S'A!A JbA@S'A8A>k|AduA|A+mA=AوAYAqfAAMZaAl% A|BA&AWG@AMT@.AɊ6ABAz+ALA%@AA ʍA@lA|AU0AqfApA#A'wxAA6lABAn@0 A|2A&#A#AiA)AYA!AYAC AYAA5AHA>AlAILA)AA(ADA=4A AtA8AAA/A=WAUAw= AA|AA[AAqfAPaA-:A'HA|"Aޖ]AzY3A5ACALA+gASoAAZ@AdA}aAuԉAAxA,iAAaA AAqfA3AʩAA\AwA?AFaAA3YAhAaA*@ArA+dA+WA+dAوSAFTA5A¼AAgAi>ArAAAۑA؍A+A AAaAl ABAPA A'xAlęASA۪A?AAƦAj@Ac@إA|bAU(AوCAA{"`A| #AAAWA*A=Ag A\A?!pALA̔YAA.pA2DA0CAVAVaAͯA]A4TAAbbA%AIAXAA@'xA~A&oAfA4aA@YA_AYAAiFA@LA+A>kTAوCA(AiAYA7AO6Al%5A+wAiAO@8AA 0A}A&oA@,A=WA}_NAJ@LA!AA"OAʙFAn@BAMZIA˔AA7AϞAxAAAAYA*AAAAA ʍA@A|rAA6A;GAA>kLAOA<]A)AӍAAʙnAqA/A%A5A6AEHA3AACuABAW@BA@LAT_~AODA.Aq{A|bAe=AΓA+dA!A}zA7@AAAѣADASoA8A^8AޑA>'AA0CAK}`AAriA0A̦]AAWAAAAAZAA A+WA$AEAAWMA3AgD A=A YAԪAAjAxAAWAA2zAAAsAAS'AᕋAYA+oAq{AduAJAAAو#AZ0TA*Aʙ6AqVA#|wAAjAaA^\ApAsAeEjAPALACDA}XA8@_OA/^AjA8A5AWAl%=A(@VVA&@AH@؍ACDAA/@$[A@鄒A;@'xA|*AAd%A~A6AF A_đAթAЃAApAlA@yA"A;A5AdmALA'AAوA+dA+A3>xA:AgA=CA@A/*AA6kTA|rAAP A>kLA+gAe/|A/@'xAW@PAu $ADA̗A A UAoALABAC\AA> AAlĕA AhAƨAAAaAF#A@A'AA؍A۶AjA֯A O\A[ޑAAyAq{A@A~A5AWAAPABA@ 0AޑASgA|BAA8A0AHOA#ASAʙ&A=@@A!AFSA3@G^A!k8AA3s5ASoA@\jA1@AgAAAA[AdAזAϧ8A~(4Al1A7AA9AAk@KӱAW@yaAmA>kTAPAS/AUgAwAbA A\5A5A8A.AA'xAMZ9A'pAd5A±AW@PaAUAAGEABAq>AT[Ae@|zADAAdmA<AlĕA^eADiA AO&5AqݍA1A(ARA NAAbAAۢA:KwAOAAqVAqA'AA iAgA{6AnA؍AᕓAהA>Au @A0ArA+ACÁAAdAVA؃Aʙ>ARAU(AMZqAAx#A׍Ai˅A2>A%AKA!AtVABAAT@A,ADABA?wAI*fA"A[DAԴAA3[AAA~AƦARAA|AA*AAAsAA5ACAEAZ˕AAۂA>A޴bAAcƄAE0A AA8A'AA'A:FAAzABAmĵAAAÃAeALmzAٖA&@KACAAMHA'XAMZ AAEA}'A/@SAV~?A `A@BAو3ArčAa,AA@A5z@l% ArAdAAAOGA_>A>k|A'AaAUgALAv7AAlęAjAdTAxAzOA'xAAA•AAAYAT@框A\|AAGAaAt:Au֮A6=A6DAAkTAC,A5FA= A*TAkAGdAbAA~AASAp[TA12A U ALA[A:A>klA!A>A;AA3ASGA+WA"A5@MLA%\AGdAoZ Aʙ>Ad%A+"A@RAa,ARٱARABAdAA*A@5A)mAAt:ATAKriABAAl>YA,bAw'Ae+AAԜAAq6AJWAsAA/AAbATA7MAA(/A$AAWAA؅Aq6AYA> A8ADyAAᕗAAnA*AF&AYA~AxA)A@dAAA@>xAAhpA:/AqAcGA!nAwAqݍAwA+A+_xAԪ@YAC AYA8APLAAAAAh٣AA^NA#AHȡA/AAQ4A @OA _A!(A-&AA+mVAUpA|rA~6pAiAAA8ݵ@ɪAB)@ӛAǓA3(AVMA=ArAA+AA+GAA!AA"AYAd5AFAJ*AA`@Aˏ@`nAaAAjAAbjA] A؝APAAMZ9A.֟AAA1rA"A: AS'AfAZA&Ad4A!#A4AARy/A3BAY0A_@A#oAA6|AAAAr @XAqAA+wAjA(@SwAW@YMik}l[  Aaj*_7f%L\e"*L"f%&8nRq53Q8+,aco&l!34G#xd-;T>SX9@niQV~H~ihG+Mr#;RQRr&CsVBhd?}6}!GY[w72m_bMhCmxOf Z{Kkqfy$W 8bx!\cg/OqRKl~!qP*p/;?.(0aBuPf/M8EP,)ep,S @p} D[1.97ZjI|W_h<2Ou*fi #AaN89[p(A<kQB?@02]8+:jCEF*&r$AwZHQSF0+4t TWaS^(qm Otf^jl;[mjsF7s!zlC6t!| Urs\JLb yKot%eH ]x{#D)/_i$/imO? `r[OgKh4bB0pu'x9z yItZ27a'&3'=wm/@uA  1Yo]3=56:IK%c#j eGeu5UV=9T7Z1o5{<_V" "Iqn&kHyUeHXnK< e}vwM&^v@8U/@QEb?}L,$1:;? nI$:6f)*vI/9..S9W EW|5!\jb<>xht8BD>G>sjm m~LNc]![tX@oVW13 5iw)Q]aT eT;3fzjmW=UT*V"^qr:=Cw> 2hz| 194By'ms n;[+] V>LUb'K HdT"ugVOAgoN<}qnJ/"ywU-.cgE56("rXP<>B1`o&BDHNK$IKe]*,-SN5`?UW6: Z\1M`clR gi@Y Gp%:np\s}?uvAdz|LyV`i2sM1ugdq~w6W&@2#[GT+`YK uv  v,647@-!K0N-\; g>u\!MR6$46a*<>, "4OX|3pBC9GHd=?BGNO2CEm$8vRT`JS)8OPX\])(TkAceF5h']1. #5*opGLhcxUlXmo9&tt}~z8~MY[V}4)MNW$XtY`K}{g,A*(F%.?hik -I-D #GxE-#v%Rf?wGH"R_|gr$:) |1S] 7lqJL@)xF'PF<~VLNY=J*- P?E?bRXgUc ,^ drt,w nmy>R {e%w lh. {Pf,!28OIC C%'Du -Z4~ d(2GJns]zS67wIg= R:A+CEn`HI )0 OP&o7MST~Y[d\i8w_`5LGf]A`(knMfPr4sOxm#+yNhMT|h}~a{oJYx[Y2^<b/YdVd\66^4\%;mq3 I  kE<9!z@r/jbR>#7CH(=c}i>,.jkk`":q3_Y9:X W@AIA[ hPo3$XbJKW0QNoBUZ|Z]+^%:)2h ]\opR^DDv~v=HE_(9$zW*$Bg'_J`alC>( 'v1(/pK}/DU\z^ =Hq ]ƒ́eW }+r+0fZ܁gHh0'߃Yށ !S +,^o-I$w4+$y,=&ӂx) ҂aD*Azv}Ѐo[4Klt-1~R._2r%a\U29Z.Lh/:[D#b`%Z&Xgu%X^̀8M9ebф;ir#)<,=ځ&" .gi]|\cUJ%8DQWF7 jYF4 ł<#"c ~Hw d+Yk)@p7p8(x{a`|N  /L"oY@IG< * BԄ__2Ą0OzuAfT@qw1 #5vxhc!wCdd`J}8P9yTǁ6ud;EeK3>1u|(bLvt &c!ރ$Q72-g̃Bo WV\.11`t'*V3(~V ~<P6x!!=/.G>̀ -5?܄@vO88?J܃k{4F j0' ={5؀%5H* UmJ 7xP:wjNB`]Tl _׃AO3xa6=|~Y:>{ )T$:Ƃ)#of}WcEg9_ aq?Ä#KOmRi"FI,LfE:yL@^C;'DB:΀n[ GzI1u8G]ȃp&6=Qނi~̂L]e(dtIsP?^iK:<L=V@qbt> d<g ڂAʁTesBCPtQSUjoxm'r}n%8/FlHs!qksWCF>SCSDÁJXm0T)TZHsSBKpʃGjM &Łw͂R@&![oz2A9EN(l"M4'3h+,#h;Q WkXMӃ9lԀ|ۃI{oE6Ȅ%\ ( āq9r,m br݁C*%Mhcu$m]!nvR>V[R*ڄ V2y, Zׄ[x ;NƁ\(΃z{'{QAfF@DA@"ArialNew RomanCopyright GlassSorcery 2006