A ring of 101 cubes is established by placing a cube on the faces of small rhombicosidodecahedron. The the ring is repeated with increasing size so that the faces of cubes coincide or meet at their vertices.
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Manipulate[fi=1.618;alf=ArcTan[fi];bet=ArcTan[1/fi];bet1=ArcTan[1/fi^2];y=0.5+0.5fi;x=y/fi;rte=Sqrt[x^2+y^2];el=yfi;srd=GraphicsComplex[PolyhedronData["SmallRhombicosidodecahedron","VertexCoordinates"],Polygon[PolyhedronData["SmallRhombicosidodecahedron","FaceIndices"]]];srdn=Rotate[Rotate[srd,bet,{0,1,0}],Pi,{0,0,1}];u=fi/2;s=u/Tan[2Pi/20];cub=GraphicsComplex[PolyhedronData["Cube","VertexCoordinates"],Polygon[PolyhedronData["Cube","FaceIndices"]]];cub0={Rotate[Rotate[Scale[cub,1{1,1,1},{0,0,0}],bet,{1,0,0}],2Pi/5,{0,0,1}]};cuba=Translate[Rotate[cub0,-4Pi/5,{0,0,1}],{-u,0,0}];cubb=Translate[cub0,{u,0,0}];cub10=Table[Rotate[Translate[{cuba,cubb},{0,s,0}],i2Pi/5-Pi/10,{0,0,1}],{i,5}];cubring=Table[{Hue[0.56^i],Scale[cub10,1.48^i{1,1,1},{0,0,0}]},{i,4}];Graphics3D[Rotate[{cub10,cubring,Yellow,srdn},rot,{0,1,0}],BoxedFalse,SphericalRegionTrue,ViewAngle0.01,ViewPoint{0,0,100}],{{rot,0,"rotate"},0,3.14},TrackedSymbols->rot]
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