Truncated rhombihedron

The truncated rhombihedron, hyperhombicosicosahedron, tar, or compound of five truncated cubes is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 30 octagons, with one triangle and two octagons joining at each vertex. As the name suggests, it can be derived as the truncation of the rhombihedron, the compound of five cubes.

Its quotient prismatic equivalent is the truncated cubic pentachoroorthowedge, which is seven-dimensional.

Vertex coordinates
The vertices of a truncated rhombihedron of edge length 1 can be given by all permutations of: along with all even permutations of:
 * $$\left(\pm\frac{1+\sqrt2}{2},\,\pm\frac{1+\sqrt2}{2},\,\pm\frac12\right),$$
 * $$\left(\pm\frac{\sqrt2+\sqrt{10}}{8},\,\pm\frac{-2-\sqrt2+2\sqrt5+\sqrt{10}}{8},\,\pm\frac{1+\sqrt5+\sqrt{10}}{4}\right),$$
 * $$\left(\pm\frac{\sqrt2}{4},\,\pm\frac{-2-3\sqrt2+2\sqrt5+\sqrt{10}}{8},\,\pm\frac{2+3\sqrt2+2\sqrt5+\sqrt{10}}{8}\right),$$
 * $$\left(\pm\frac{2+\sqrt2}{4},\,\pm\frac{4+3\sqrt2-\sqrt{10}}{8},\,\pm\frac{4+3\sqrt2+\sqrt{10}}{8}\right),$$
 * $$\left(\pm\frac{2+\sqrt2+2\sqrt5+\sqrt{10}}{8},\,\pm\frac{\sqrt2-\sqrt{10}}{8},\,\pm\frac{-1+\sqrt5+\sqrt{10}}{4}\right).$$