Small icosicosahedron

The Small icosicosahedron, se, or compound of five octahedra is a uniform polyhedron compound. It consists of 40 triangles which form 20 coplanar pairs, combining into golden hexagrams. 4 triangles join at each vertex.

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

It can be derived as a rectified chiricosahedron. It is also related to the icosicosahedron. If each stella octangula in the icosicosahedron is replaced with the intersection of the two tetrahedra (an octahedron), the result is a small icosicosihedron.

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

Vertex coordinates
The vertices of a small icosicosahedron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * (±$\sqrt{2}$/2, 0, 0)
 * (±$\sqrt{6}$/4, ±($\sqrt{2}$+$\sqrt{2}$)/8, ±($\sqrt{2}$–$\sqrt{2}$)/8)