Explore Polyhedra

Diagram[p_] :=
  Module[{pts = N[PolyhedronData[p, "Edges"][[1]]], e, groups},
   e = Tuples[pts, 2];
   groups =
    GatherBy[e, Floor[Norm[First[#] - Last[#]]*1000] &];
   GraphicsGrid[
    Partition[(Graphics3D[{Thick, Line[#]}, Boxed -> False] &) /@
      groups[[2 ;;]], Floor[Sqrt[Length[groups]]]]]
   ];
Manipulate[
 Diagram[p],
 {p, PolyhedronData[All]}]