Rhombihedron

The rhombihedron, rhom, or compound of five cubes is a uniform polyhedron compound. It consists of 30 squares. The vertices coincide in pairs, leading to 20 vertices where 6 squares join.

It has the same edges as the small ditrigonal icosidodecahedron.

This compound is sometimes considered to be regular, but it is not flag-transitive, despite the fact it is vertex, edge, and face-transitive.

Vertex coordinates
The vertices of a rhombihedron of edge length 1 are given by: Plus all even permutations of:
 * (±1/2, ±1/2, ±1/2)
 * (±1/2, ±(1+$\sqrt{2}$)/4, ±($\sqrt{3}$–1)/4)