Symmetries of an 54-faced solid
Sándor Kabai
The symmetries of a 54-faced solid is shown.
The symmetries of a 54-faced solid is shown.
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Manipulate[f=1.618;vA={f,-f,0};vB={f,0,0};vC={f,0,f};vD={f,-f,f};vE={0,0,0};vF={0,0,f};vG={0,-f,f};vH={0,-f,0};vO={f/2,-f/2,f/2};vAB={f,-1/f-a,0};vBC={f,0,1-a};vCF={1/f+a,0,f};vFG={0,-1+a,f};vGH={0,-f,1/f+a};vHA={1-a,-f,0};c1=Polygon[{vA,vAB,vBC,vC,vD}];c1s=Polygon[{vAB,vBC,vB}];c2=Polygon[{vE,vB,vBC,vCF,vF}];c2s=Polygon[{vBC,vC,vCF}];c3=Polygon[{vE,vH,vGH,vFG,vF}];c3s=Polygon[{vG,vFG,vGH}];c4=Polygon[{vD,vG,vGH,vHA,vA}];c4s=Polygon[{vH,vHA,vGH}];c5=Polygon[{vC,vCF,vFG,vG,vD}];c5s=Polygon[{vF,vFG,vCF}];c6=Polygon[{vE,vB,vAB,vHA,vH}];c6s=Polygon[{vA,vHA,vAB}];t1=Polygon[{vAB,vBC,vO}];t2=Polygon[{vO,vBC,vCF}];t3=Polygon[{vO,vCF,vFG}];t4=Polygon[{vO,vFG,vGH}];t5=Polygon[{vO,vGH,vHA}];t6=Polygon[{vO,vHA,vAB}];spFG={Green,Sphere[vFG,dia1]};spGH={Yellow,Sphere[vGH,dia1]};spHA={RGBColor[0.3,0.8,1],Sphere[vHA,dia1]};spO={RGBColor[1,0.4,0.5],Sphere[vO,dia2]};u1=Translate[{spO,spFG,spGH,spHA,c1s,c2,c3,c4s,c5s,c6,t1,t2,t3,t4,t5,t6},{0,-div3,0}];right={spO,spFG,spGH,spHA,c1,c2s,c3s,c4,c5,c6s,t1,t2,t3,t4,t5,t6};u2=Translate[Rotate[{right},-Pi,{0,1,0},{0.809,-0.809,0.809}],{0,div3+1.618,0}];u34=Translate[Rotate[{u1,u2},Pi,{0,0,1}],{div2,0,0}];u5678=Translate[Rotate[{u1,u2,u34},Pi,{1,0,0}],{0,0,div1}];Graphics3D[{{RGBColor[0.7,1,0.5],Translate[If[rights,{right},{}],{s,-s-div3,s}]},u1,u2,u34,u5678},BoxedFalse,ViewPoint{-4,-4,4},PlotRange2.6,ViewAngle0.14],{{a,0,"modify triangles"},-0.618,0.19},{{rights,True,"show outside matching unit"},{True,False}},{{s,0,"separate outside matching unit"},0,0.4},{{div1,0,"divide 1"},0,-0.6,ImageSizeTiny,ControlPlacementLeft},{{div2,0,"divide 2"},0,-0.6,ImageSizeTiny,ControlPlacementLeft},{{div3,0,"divide 3"},0,0.4,ImageSizeTiny,ControlPlacementLeft},{{dia1,0.1,"diameter 1"},0,1,ImageSizeTiny,ControlPlacementLeft},{{dia2,0.15,"diameter 2"},0,1,ImageSizeTiny,ControlPlacementLeft},TrackedSymbolsManipulate]
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