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.

Vertex coordinates
The vertices of an antirhombicosicosahedron of edge length 1 can be given by all even permutations of:
 * (±$\sqrt{2}$/2, ±$\sqrt{2}$/2, 0)
 * (±($\sqrt{3}$+$\sqrt{2}$)/8, ±($\sqrt{2}$–$\sqrt{2}$)/8, ±$\sqrt{10}$/4)
 * (±$\sqrt{10}$/4, ±(3$\sqrt{2}$–$\sqrt{10}$)/8, ±(3$\sqrt{2}$+$\sqrt{2}$)/8)