Antirhombicosicosahedron

The antirhombicosicosahedron, arie, or compound of five cuboctahedra is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 30 squares, with two of each joining at a vertex.

It can be thought of as a rectification of either the small icosicosahedron or the rhombihedron, or the cantellation of the chiricosahedron.

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

Vertex coordinates
The vertices of an antirhombicosicosahedron of edge length 1 can be given by all even permutations of:
 * $$\left(\pm\frac{\sqrt2}{2},\,\pm\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(\pm\frac{\sqrt2+\sqrt{10}}{8},\,\pm\frac{\sqrt{10}-\sqrt2}{8},\,\pm\frac{\sqrt{10}}{4}\right),$$
 * $$\left(\pm\frac{\sqrt2}{4},\,\pm\frac{3\sqrt2-\sqrt{10}}{8},\,\pm\frac{3\sqrt2+\sqrt{10}}{8}\right).$$