Rhombisnub rhombicosicosahedron

The rhombisnub rhombicosicosahedron, rasseri, or compound of five small rhombicuboctahedra  is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 30+60 squares, with one triangle and three squares joining at each vertex. It can be seen as the cantellation of the rhombihedron.

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

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