Sándor Kabai
Cluster of 212 rhombic triacontahedra (RT)
Rings of RT are associated with the 120 RT located at the vertices of great rhombicosidodecahedron. 222 RTs are in the assembly altogether, which is reated to various polyhedra (120 + 60 + 20 + 12).
Cluster of 212 rhombic triacontahedra (RT)
Rings of RT are associated with the 120 RT located at the vertices of great rhombicosidodecahedron. 222 RTs are in the assembly altogether, which is reated to various polyhedra (120 + 60 + 20 + 12).
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fi=GoldenRatio;alf=ArcTan[fi];bet=ArcTan[1/fi];bet1=ArcTan[1/fi^2];y=Sin[alf];x=Cos[alf];u=yfi;s=u/Tan[2Pi/20];v=N[m/2/Sin[2Pi/10]];m=2yfi;d=x/Tan[2Pi/10];p=x/Sin[2Pi/10];k=Sqrt[(2d+p)^2-u^2];h=Sqrt[m^2-(p+2d)^2];ico=PolyhedronData["Icosahedron","Faces"];icov=PolyhedronData["Icosahedron","VertexCoordinates"];rt=PolyhedronData["RhombicTriacontahedron","Faces"];rtn=Rotate[rt,Pi,{0,0,1}];rtf=Rotate[Rotate[rt,bet,{0,1,0}],0Pi/2,{0,0,1}];rh=PolyhedronData["RhombicHexecontahedron","Faces"];rh1=Translate[rh,{0,0,fi^2}];grd=PolyhedronData["GreatRhombicosidodecahedron","Faces"];grdn=Rotate[grd,bet,{0,1,0}];
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rtc=Translate[rt,{p+2d,0,h}];rt5=Table[Rotate[{rtc},i2Pi/5,{0,0,1}],{i,5}];Graphics3D[{Red,rt,Cyan,rt5},ViewPoint{100,0,0},ImageSize200,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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rta=Translate[rt,{0,u,0}];rtb=Translate[rt,{0,-u,0}];rt10=Table[Rotate[Translate[{rta,rtb},{s,0,0}],i2Pi/5,{0,0,1}],{i,5}];Graphics3D[{Yellow,rt10},ViewPoint{0,0,100},ImageSize300,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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Graphics3D[{Red,rt,Cyan,rt5,Yellow,rt10},ViewPoint{0,0,100},ImageSize300,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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rts=Translate[rt,{s+k,0,-u}];rtab=Translate[{rta,rtb},{-s-2d-p,0,-u}];rt15=Table[Rotate[{Green,rtab,Pink,rts},i2Pi/5,{0,0,1}],{i,5}];Graphics3D[{rt15},ViewPoint{0,0,100},ImageSize300,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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Graphics3D[{RGBColor[0.8,0.8,0.3],rh1,Red,rt,Cyan,rt5,Yellow,rt10,rt15},ViewPoint{0,0,100},ImageSize300,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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r1=Table[Rotate[Translate[rtab,{2(s+2d+p)+2d,0,-u}],i22Pi/5,{0,0,1}],{i,5}];r2=Table[Rotate[Translate[rtab,{-2d-p,0,-u}],i22Pi/5,{0,0,1}],{i,5}];Graphics3D[{rt5,rt10,rt15,r1,Yellow,r2},ViewPoint{0,0,100},ImageSize300,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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Graphics3D[{Yellow,rt15,rts,rt10,Cyan,rt5,Pink,rt},ViewPoint{0,0,100},ImageSize400,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]