Today, I discovered an interesting compound of J63, the tridiminished icosahedron.

Take four J63's, centered on the origin, oriented according to the symmetries of a regular tetrahedron. Then all their triangular faces will be disjoint and form a closed polyhedral surface in the shape of an inscribing regular icosahedron. Furthermore, their pentagonal faces together form the non-convex great dodecahedron.

One might be tempted to express this relationship with the (pseudo-)equation:

o5o3x + x5o(5/2)o ≡ 4 * J63