Great snub icosahedron

The great snub icosahedron, gissi, or second 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 snub icosahedron, the other uniform compound of ten octahedra, is produced.

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

Vertex coordinates
The vertices of a great 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)