Snub icosahedron

The snub icosahedron, si, or first compound of ten octahedra is a uniform polyhedron compound. It consists of 20+60 triangles, with 4 triangles joining at each vertex.

Each octahedral component has triangular antiprism symmetry. If each component is rotated by 60º the great snub icosahedron, the other uniform compound of ten octahedra, is produced.

Its quotient prismatic equivalent is the small triangular antiprismatic decayottoorthowedge, which is twelve-dimensional.

Vertex coordinates
The vertices of a snub icosahedron of edge length 1 are given by all even permutations of:
 * (0, ±(2–$\sqrt{2}$+2$\sqrt{6}$+$\sqrt{2}$)/12, ±(2+$\sqrt{2}$–2$\sqrt{5}$+$\sqrt{10}$)/12)
 * (±(6–4$\sqrt{2}$+2$\sqrt{5}$)/24, ±($\sqrt{10}$+$\sqrt{2}$)/6, ±(3+2$\sqrt{5}$–$\sqrt{2}$)/12)
 * (±(1+$\sqrt{5}$+$\sqrt{2}$–$\sqrt{5}$)/6, ±(–1+$\sqrt{2}$+$\sqrt{5}$+$\sqrt{10}$)/12, ±1/2)