The faces of polyhedra are reduced in size in their own plane. Frame polyhedra can be produced when shown together with the original polyhedra. In case of rhombic triacontahedron the size change leads to another polyhedron (great rhombic triacontahedron).
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shrink[t_,Polygon[x_List,opts___]]:=Module[{c=Plus@@x/Length[x]},Polygon[Map[(c+(1-t)(#-c))&,x],opts]]
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tico=PolyhedronData["TruncatedIcosahedron","Faces","Polygon"];​​ticosr={tico/.y_Polygonshrink[0.14,y]};​​Graphics3D[{ticosr},BoxedFalse,SphericalRegionTrue,ImageSize200]
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Graphics3D[{Cyan,tico,Yellow,Scale[ticosr,1.01]},BoxedFalse,SphericalRegionTrue,ImageSize200]
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Manipulate[​​rt=PolyhedronData["RhombicTriacontahedron","Faces","Polygon"];​​rtsr={rt/.y_Polygonshrink[exp,y]};​​Graphics3D[{rt,Yellow,rtsr},BoxedFalse,SphericalRegionTrue,ImageSize300],​​{{exp,0,"expand"},-3.23,0.5},​​TrackedSymbols->exp,SaveDefinitions->True]
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​
expand
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Manipulate[​​p=PolyhedronData[PolyhedronData[][[nn]],"Faces","Polygon"];​​sr={p/.y_Polygonshrink[0.4,y]};​​Graphics3D[{p,Green,Scale[sr,1.01]},BoxedFalse,SphericalRegionTrue,ImageSize300],​​{{nn,10,"no"},1,215,1,RadioButton},​​TrackedSymbols->nn,SaveDefinitions->True]
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​
no
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In[]:=
poly=PolyhedronData[];​​name=PolyhedronData[#,"Name"]&/@PolyhedronData[];​​pop=Transpose[{poly,name}]/.{a_,b_}Rule[a,b];​​Manipulate[​​ID=PolyhedronData[nn,"Name"];​​what=PolyhedronData[nn,"Faces","Polygon"];​​sh={what/.y_Polygonshrink[exp,y]};​​​​Graphics3D[{what,Cyan,Scale[sh,1.001]},BoxedFalse,SphericalRegionTrue,ViewPoint{0,0,100},ViewAngle0.01,ImageSize400,PlotLabelID],​​{{nn,"RhombicTriacontahedron","polyhedron"},Evaluate@pop},​​{{exp,0.5,"expand"},-3.23,0.9},​​TrackedSymbols{nn,exp},SaveDefinitions->True]
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​
polyhedron
rhombic triacontahedron
expand