RT[a_,p_]:={RotationTransform[a,{0,1,1}]/@p[[1]]//N};
PT[p_,a_]:=Table[Tube[Table[(a/Pi)*RT[a,p][[1,p[[2,j,i]]]],
{i,Length[p[[2,j]]]}],.03],{j,Length[p[[2]]]}]
GT[p_,n_]:=Graphics3D[Table[{Hue[i/n],PT[p,2i*Pi/n]},{i,n}],
Boxed->False,ImageSize->600];
GT[BeveledPolyhedron[Dodecahedron[],.5],5]
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