One RH is placed at each of the 32 vertices of RT. The gaps between the RHs (along the edges of RT) are filled with RT or RT-RH pairs to create a frame RT.
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(*varyntochangetheedgelengthofframeRT*)n=1;β=ArcTan[0.618];r=(n+1)2×2.618Cos[β]/Sin[β];rh=PolyhedronData["RhombicHexecontahedron","Faces"];rtv=PolyhedronData["RhombicTriacontahedron","VertexCoordinates"];rh32=Map[Translate[rh,#]&,r/1.618*rtv];rt=PolyhedronData["RhombicTriacontahedron","Faces"];rtd=Translate[rt,{0,0,-2.618}];rtds=Table[Translate[{{Yellow,rh},{RGBColor[0,1,1],rtd}},{0,0,-22.618i}],{i,n}];rt5=Table[Rotate[Rotate[{rtd,rtds},2β,{0,1,0}],i2Pi/5+2Pi/10,{0,0,1}],{i,5}];up={RGBColor[0,1,1],Translate[{rt5},{0,0,r}]};up5=Table[Rotate[Rotate[up,2β,{0,1,0}],i2Pi/5+2Pi/10,{0,0,1}],{i,5}];down=Rotate[{up5,up},Pi,{0,1,0}];rtbig=Scale[rt,(1+n)4.8{1,1,1},{0,0,0}];Graphics3D[{rtbig,up,up5,down,{Yellow,rh32}},Boxed->False,SphericalRegionTrue,ViewPoint{0,0,100},ViewAngle0.01,ImageSize400]
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Graphics3D[{{rtbig,Yellow,rh32}},Boxed->False,SphericalRegionTrue,ViewPoint{0,0,100},ViewAngle0.01,ImageSize400]
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Graphics3D[{Glow[White],rtbig,up,up5,down,{Yellow,rh32}},Boxed->False,SphericalRegionTrue,ViewPoint{0,0,100},ViewAngle0.01,ImageSize400]
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