Ten RDs are arranged in a ring with edge to edge connection. The tips of the RDs are at the vertices of two IDs. The centers of RDs are at the vertices of an intermediate IDs. The sizes of IDs are relation to one another in proportion of the golden ratio. The ring of ten RDs is part of a cluster of 30 RDs.
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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;​​u=fi/2;​​s=u/Tan[2Pi/20];​​rd=GraphicsComplex[PolyhedronData["RhombicDodecahedron","VertexCoordinates"],Polygon[PolyhedronData["RhombicDodecahedron","FaceIndices"]]];​​rdn30=Scale[Rotate[rd,Pi/4,{0,0,1}],0.86];​​rd1=Translate[{rdn30},{0,0,0.5+el}];​​rd2=Rotate[rd1,Pi,{1,0,0}];​​rd3=Rotate[Rotate[{rd1,rd2},Pi/2,{1,0,0}],Pi/2,{0,0,1}];​​rd4=Rotate[Rotate[{rd1,rd2},Pi/2,{0,1,0}],Pi/2,{0,0,1}];​​rd30=Table[Rotate[Rotate[{rd1,rd2,rd3,rd4},bet,{1,0,0}],i2Pi/5-Pi/2,{0,0,1}],{i,5}];​​Manipulate​​rdn10=Scale[Rotate[rd,Pi/4,{0,0,1}],exp0.861];​​rd0={Rotate[Rotate[Scale[rdn10,1{1,1,1},{0,0,0}],bet,{1,0,0}],2Pi/5,{0,0,1}]};​​rda=Translate[Rotate[rd0,-4Pi/5,{0,0,1}],{-u,0,0}];​​rdb=Translate[rd0,{u,0,0}];​​rd10=Table[Rotate[Translate[{rda,rdb},{0,s,0}],i2Pi/5-Pi/10,{0,0,1}],{i,5}];​​(*id*)​​id=GraphicsComplex[PolyhedronData["Icosidodecahedron","VertexCoordinates"],Polygon[PolyhedronData["Icosidodecahedron","FaceIndices"]]];​​id21=PolyhedronData["Icosidodecahedron","Edges"];​​idv=PolyhedronData["Icosidodecahedron","VertexCoordinates"];​​idsp=Map[Translate[Sphere[{0,0,0},0.1],#]&,idv];​​idspout=Map[Translate[Sphere[{0,0,0},0.1],#]&,2.2idv];​​idspfi=Map[Translate[Sphere[{0,0,0},0.1],#]&,fiidv];​​idfr={Map[Cylinder[idv[[#]],0.02]&,id21]};​​idfifr=Scale[idfr,fi];​​idoutfr=Scale[idfr,2.2];​​​​Graphics3D[{If[idouts,{LightPurple,idoutfr,Yellow,idspout},{}],If[rd30s,rd30,{}],{Red,idspfi},LightGreen,id,RGBColor[0.4,1,0.3],idfifr,RGBColor[0.5,1,1],rd10,idsp},BoxedFalse,SphericalRegionTrue,ImageSize500,ViewPoint{0,0,100}],​​{{exp,1,"grow rhombic dodecahedron"},0.1,1},​​{{rd30s,False,"30 rhombic dodecahedra"},{True,False}},​​{{idouts,True,"outside icosidodecahedron"},{True,False}},​​TrackedSymbols{exp,rd30s,idouts},ControlPlacement->Top,SaveDefinitions->True
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grow rhombic dodecahedron
30 rhombic dodecahedra
outside icosidodecahedron
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Graphics3D[{rd10,idsp,LightGreen,id},BoxedFalse,SphericalRegionTrue,ImageSize500,ViewPoint{0,0,100}]
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Graphics3D[{idspout,Pink,idsp,Green,idoutfr,LightPurple,rd10,LightGreen,id},BoxedFalse,SphericalRegionTrue,ImageSize500,ViewPoint{0,0,100}]
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Graphics3D[{rd10,Pink,idsp},BoxedFalse,SphericalRegionTrue,ImageSize500,ViewPoint{0,0,100}]
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