Rhombisnub icosahedron

The rhombisnub icosahedron, rosi, or compound of ten hexagonal prisms is a uniform polyhedron compound. It consists of 60 squares and 20 hexagons, with one hexagon and two squares joining at a vertex.

Its quotient prismatic equivalent is the ditrigonal trapezoprismatic decayottoorthowedge, which is twelve-dimensional.

Vertex coordinates
The vertices of a rhombisnub icosahedron of edge length 1 are given by all even permutations of:
 * $$\left(\pm\frac12,\,\pm\frac{3+\sqrt3+3\sqrt5-\sqrt{15}}{12},\,\pm\frac{-3+\sqrt3+3\sqrt5+\sqrt{15}}{12}\right),$$
 * $$\left(\pm1,\,\pm\frac{\sqrt{15}-\sqrt3}{12},\,\pm\frac{\sqrt3+\sqrt{15}}{12}\right),$$
 * $$\left(\pm\frac{3+\sqrt3}{6},\,\pm\frac{3-2\sqrt3+3\sqrt5}{12},\,\pm\frac{-3+2\sqrt3+3\sqrt5}{12}\right),$$
 * $$\left(\pm\frac{3+\sqrt3–3\sqrt5+\sqrt{15}}{12},\,\pm\frac12,\,\pm\frac{3-\sqrt3+3\sqrt5+\sqrt{15}}{12}\right),$$
 * $$\left(\pm\frac{-3-2\sqrt3+3\sqrt5}{12},\,\pm\frac{3-\sqrt3}{6},\,\pm\frac{3+2\sqrt3+3\sqrt5}{12}\right).$$