Compound of five cubes

The compound is a faceting of a dodecahedron (where pentagrams can be seen correlating to the pentagonal faces).

Each cube represents a selection of 8 of the 20 vertices of the dodecahedron.

Its convex hull is a regular dodecahedron.

With these, it can form polyhedral compounds that can also be considered as degenerate uniform star polyhedra; the small complex rhombicosidodecahedron, great complex rhombicosidodecahedron and complex rhombidodecadodecahedron.

The compound of ten tetrahedra can be formed by taking each of these five cubes and replacing them with the two tetrahedra of the stella octangula (which share the same vertex arrangement of a cube).