Cluster of 30 cubes
Sándor Kabai
One cube is placed on each of the 30 square face of a Small Rhombicosidodecahedron. This structure could be the basis for a wide ranging exploration of possible structures. Recommended routes: replace cube with equivalent polyhedra, connect vertices, fill spaces, find envelopes.
One cube is placed on each of the 30 square face of a Small Rhombicosidodecahedron. This structure could be the basis for a wide ranging exploration of possible structures. Recommended routes: replace cube with equivalent polyhedra, connect vertices, fill spaces, find envelopes.
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fi=GoldenRatio;bet=ArcTan[1/fi];el=N[(fi+fi^2)/2];srd=GraphicsComplex[PolyhedronData["SmallRhombicosidodecahedron","VertexCoordinates"],Tube[PolyhedronData["SmallRhombicosidodecahedron","FaceIndices"],0.1]];srdn=Rotate[Rotate[srd,bet,{0,1,0}],Pi,{0,0,1}];cub=GraphicsComplex[PolyhedronData["Cube","VertexCoordinates"],Polygon[PolyhedronData["Cube","FaceIndices"]]];c1=Translate[cub,{0,0,0.5+el}];c2=Rotate[c1,Pi,{1,0,0}];c3=Rotate[Rotate[{c1,c2},Pi/2,{1,0,0}],Pi/2,{0,0,1}];c4=Rotate[Rotate[{c1,c2},Pi/2,{0,1,0}],Pi/2,{0,0,1}];cub30=Table[Rotate[Rotate[{c1,c2,c3,c4},bet,{1,0,0}],i2Pi/5-Pi/2,{0,0,1}],{i,5}];cub30t=cub30/.Polygon->Tube;Graphics3D[{Yellow,cub30t,Pink,cub30,Cyan,srdn},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100}]
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Graphics3D[{Yellow,cub30t,Cyan,srdn},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100}]
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Graphics3D[{Yellow,srdn,Cyan,srdn},Boxed->False,SphericalRegion->True]
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Graphics3D[{Cyan,cub30},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100}]
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(*elistheheightofthesquareofsrd*)N1+
5
2
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2.11803
(*srdvetrices*)srd;