Chirorhombidodecahedron

The chirorhombidodecahedron, rhombidodecahedron, kred, or compound of six pentagonal prisms is a uniform polyhedron compound. It consists of 30 squares and 12 pentagons, with one pentagon and two squares joining at a vertex.

Its quotient prismatic equivalent is the pentagonal prismatic hexateroorthowedge, which is eight-dimensional.

Vertex coordinates
The vertices of a chirorhombidodecahedron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(\pm\sqrt{\frac{5-2\sqrt5}{20}},\,\pm\sqrt{\frac{5+2\sqrt5}{20}},\,\pm\sqrt{\frac{5+2\sqrt5}{20}}\right),$$
 * $$\left(0,\,\pm\sqrt{\frac{5-\sqrt5}{40}},\,\pm\sqrt{\frac{5+\sqrt5}{8}}\right),$$
 * $$\left(\pm\sqrt{\frac{5-\sqrt5}{40}},\,\pm\sqrt{\frac{5+\sqrt5}{40}},\,\pm\sqrt{\frac{5+\sqrt5}{10}}\right).$$

Related polyhedra
This compound is chiral. The compound of the two enantiomorphs is the disrhombidodecahedron.