Two structurally identical assemblies are created, where the outside is larger by the golden ratio. In each assembly 60 icosahedra are connected to a frame icosidodecahedron. When the icosahedra are enveloped by by tetrahedra, then the inside vertices of the tetrahedra in the larger assembly are connected to the small assembly at the vertices of the icosidodecahedron.
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fi=1.618;alf=ArcTan[fi];bet=ArcTan[1/fi];id=GraphicsComplex[PolyhedronData["Icosidodecahedron","VertexCoordinates"],Polygon[PolyhedronData["Icosidodecahedron","FaceIndices"]]];ico=GraphicsComplex[PolyhedronData["Icosahedron","VertexCoordinates"],Polygon[PolyhedronData["Icosahedron","FaceIndices"]]];tet=GraphicsComplex[PolyhedronData["Tetrahedron","VertexCoordinates"],Polygon[PolyhedronData["Tetrahedron","FaceIndices"]]];ManipulateModule{id21,idv,idfr,idcent,idout,idfrcent,idfrout,idsp,idspout,tetn,icoc,v1,v5,v6,v25,v30,tet60,tet60cent},(*id*)id21=PolyhedronData["Icosidodecahedron","Edges"];idv=PolyhedronData["Icosidodecahedron","VertexCoordinates"];idfr={Map[Cylinder[idv[[#]],0.03]&,id21]};idcent={RGBColor[1,0.5,1],Scale[id,fi]};idout={RGBColor[1,0.5,1],Scale[id,fi^2]};idfrcent={Scale[idfr,fi]};idfrout={Specularity[0.6],RGBColor[0.5,1,0.4],Scale[idfrcent,fi]};idsp={Red,Map[Sphere[#,0.15]&,fiidv]};idspout={Red,Map[Sphere[#,0.2]&,fi^2idv]};(*tet60*)tetn=Rotate[Rotate[Scale[tet,expSqrt[2]{1,1,1},{0,0,0}],-ArcTan[Sqrt[2]],{0,1,0}],Pi/4,{0,0,1}];icoc={Rotate[Scale[Rotate[ico,alf,{0,1,0}],1.001/fi{1,1,1}],Pi/2,{0,0,1}]};v1=Translate[{tetn,Yellow,icoc},{0,0,-fi^2}];v5=Table[Rotate[Rotate[{v1},-bet,{0,1,0}],i2Pi/5,{0,0,1}],{i,5}];v6=Translate[Rotate[{v5},0,{1,0,0}],{0,0,5.5675}];v25={Table[Rotate[Rotate[Rotate[v6,Pi,{0,0,1}],-2bet,{0,1,0}],i2Pi/5,{0,0,1}],{i,5}]};v30=Rotate[{Red,v6,RGBColor[0.4,1,1],v25},Pi,{0,1,0}];tet60={v30,v6,Green,v25};tet60cent=Scale[tet60,1/fi];Graphics3D[{If[v30s,v30,{}],{Green,If[v25s,v25,{}]},If[id1,{v25,v30,idout},{}],idspout,idsp,idfrcent,idfrout,If[id2,idcent,{}],tet60cent,Red,v6},SphericalRegionTrue,ViewPoint{0,100,40},ViewAngle0.01,ImageSize400,BoxedFalse,PlotRange4.55],{{id1,True,"remove outsidde ID"},{True,False}},{{exp,0.4,"expand TET"},0.4,1.618},{{id2,True,"remove inside ID"},{True,False},ImageSize->Tiny,ControlPlacementLeft},{{v30s,False,"add 30 TET"},{True,False},ImageSize->Tiny,ControlPlacementLeft},{{v25s,False,"add 25 TET"},{True,False},ImageSize->Tiny,ControlPlacementLeft},TrackedSymbols{id1,id2,exp,v30s,v25s},SaveDefinitionsTrue
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