Rhombiquasihyperhombicosicosahedron

The rhombiquasihyperhombicosicosahedron, raquahri, or compound of five great cubicuboctahedra is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams), 30 squares, and 30 octagrams, with one triangle, one square, and two octagrams joining at each vertex.

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