Icosicosahedron

The icosicosahedron, e, or compound of ten tetrahedra is a uniform polyhedron compound. It consists of 40 triangles which form 20 coplanar pairs, combining into hexagrams. The vertices also coincide in pairs, leading to 20 vertices where 6 triangles join. It can be seen as a compound of the two chiral forms of the chiricosahedron. It can also be seen as a rhombihedron, the compound of five cubes, with each cube replaced by a stella octangula.

This compound is sometimes considered to be regular, but it is not flag-transitive, despite the fact it is vertex, edge, and face-transitive.

Vertex coordinates
The vertices of an icosicosahedron of edge length 1 are given by: Plus all even permutations of:
 * (±$\sqrt{6}$/4, ±$\sqrt{6}$/4, ±$\sqrt{2}$/4)
 * (±($\sqrt{2}$+$\sqrt{2}$)/8, ±$\sqrt{2}$/4, ±($\sqrt{2}$–$\sqrt{10}$)/8)