Cube pyramid
Sándor Kabai
Cubes and rhombic dodecahedra are arranged in a pyramid.
Cubes and rhombic dodecahedra are arranged in a pyramid.
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Manipulate[Needs["PolyhedronOperations`"];cub=GraphicsComplex[PolyhedronData["Cube","VertexCoordinates"],Polygon[PolyhedronData["Cube","FaceIndices"]]];cubn=Truncate[Scale[Rotate[Rotate[cub,Pi/4,{0,0,1}],ArcTan[Sqrt[2]],{1,0,0}],Sqrt[2]],trunc];p=Table[{2j-i,Sqrt[3]i,0},{i,0,n},{j,i,n}];If[exchange,rdn=cubn];rd=GraphicsComplex[PolyhedronData["RhombicDodecahedron","VertexCoordinates"],Polygon[PolyhedronData["RhombicDodecahedron","FaceIndices"]]];rdn=Truncate[Scale[Rotate[rd,ArcTan[Sqrt[2]],{1,0,0}],Sqrt[3/2]],trunc];If[exchange,rdn=cubn];tri1=Map[Translate[rdn,#]&,p];sp=Sphere[{0,0,0},1.1];tri2=Rotate[tri1,-Pi/6,{0,0,1}];piramid=Table[Rotate[Rotate[tri2,-ArcTan[Sqrt[2]]-Pi,{0,1,0}],i2Pi/4,{0,0,1}],{i,4}];Graphics3D[{piramid},BoxedFalse,SphericalRegionTrue,ViewAngle0.12,ViewPoint{1,-10,3}],{{n,4,"Frequency"},1,10},{{trunc,0,"Truncate cube"},0,0.5},{{exchange,True,""},{False->"RD",True->"False"},ControlPlacementLeft,ImageSize->Tiny},TrackedSymbols{n,exchange,trunc}]
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