Cube pyramids on cube
Sándor Kabai
Pyramids of cubes or rhombic dodecahedron (RD) or small rhombicuboctahedron (SRC) are placed on a cube. The contour is an octahedron. Cube, RD and SRC can be truncated to produce cuboctahedron and special SRC.
Pyramids of cubes or rhombic dodecahedron (RD) or small rhombicuboctahedron (SRC) are placed on a cube. The contour is an octahedron. Cube, RD and SRC can be truncated to produce cuboctahedron and special SRC.
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Needs["PolyhedronOperations`"];Manipulate[rd=PolyhedronData["RhombicDodecahedron","Faces"];rdn=Truncate[Scale[Rotate[rd,ArcTan[Sqrt[2]],{1,0,0}],Sqrt[3/2]],trrd];cub=PolyhedronData["Cube","Faces"];cubn=Truncate[Scale[Rotate[Rotate[cub,Pi/4,{0,0,1}],ArcTan[Sqrt[2]],{1,0,0}],Sqrt[2]],trcub];src=PolyhedronData["SmallRhombicuboctahedron","Faces"];srcn=Truncate[Scale[Rotate[Rotate[src,Pi/4,{0,0,1}],ArcTan[Sqrt[2]],{1,0,0}],0.83],trsrc];p=Table[{2j-i,Sqrt[3]i,0},{i,0,n},{j,i,n}];(*Cubecanbereplacedherewithrhombicdodecahedronorsmallrombicubocthedron*)(*cubn=rdn;orcubn=srcnorcubn=srcn;*);tri1=Map[Translate[cubn,#]&,p];tri2=Rotate[tri1,-Pi/6,{0,0,1}];pyr=Table[{Rotate[Rotate[tri2,-ArcTan[Sqrt[2]]-Pi,{0,1,0}],i2Pi/4+Pi/4,{0,0,1}]},{i,4}];cubc=Scale[cub,u(2n-1)+2u];u=Sqrt[2];p1=Translate[pyr,{0,0,(2u(n+2)/2+(n-1)u)}];p2=Table[{Hue[0.34^2i],Rotate[Rotate[p1,Pi/2,{1,0,0}],i2Pi/4,{0,0,1}]},{i,4}];p3=Rotate[p1,Pi,{1,0,0}];Graphics3D[{p1,p2,p3,RGBColor[0.8,0.7,1],cubc},BoxedFalse,SphericalRegionTrue,ImageSize400],{{n,3,"Frequency"},1,10,1,RadioButton},{{trcub,0,"Truncate cube"},0,0.5},{{trrd,0,"Truncate RD"},0,0.5},{{trsrc,0,"Truncate SRC"},0,0.5},TrackedSymbols{n,trrd,trcub,trsrc},ControlPlacement->Top]
