Cluster of 60 cubes is related to a rhombic enneacontahedron (RE) and twelve polar zonohedra (PZ). The cubes are considered as inscribed in rhombic dodecahedra (RD), which form a space filling system with RE and PZ.
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Manipulate[Module[{},rd60={rd5,rd6,rd7};cub1={RGBColor[0.2,1,1],Scale[Translate[cubn,{rte(2u+p),0,0}],size]};cub5=Translate[Table[Rotate[cub1,i2Pi/5,{0,0,1}],{i,5}],{0,0,ascent+ez}];cub6=Table[Rotate[Rotate[Rotate[cub5,Pi,{0,0,1}],-2bet,{0,1,0}],i2Pi/5,{0,0,1}],{i,5}];cub7=Rotate[{cub5,cub6},Pi,{0,1,0}];cub60={cub5,cub6,cub7};Graphics3D[{{Red,pzt},{Yellow,pz11},ren,sfrn,If[scub60,cub60,{}],If[srd60,rd60,{}]},BoxedFalse,SphericalRegionTrue,ImageSize400,ViewPoint{0,0,100},ViewAngle0.009]],{{scub60,True,"cube"},{True,False}},{{size,0.3,"cube size"},0.2,1},{{srd60,False,"RD"},{True,False},ImageSize->Tiny,ControlPlacementLeft},TrackedSymbols{srd60,scub60,size},SaveDefinitionsTrue]
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Graphics3D[{{Red,pzt},{Yellow,pz11},ren,sfrn,cub60},BoxedFalse,SphericalRegionTrue,ImageSize400,ViewPoint{0,0,100},ViewAngle0.009]
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