Great snub dodecahedron

The great snub dodecahedron, gassid, or compound of six pentagonal antiprisms is a uniform polyhedron compound. It consists of 60 triangles and 12 pentagons, with one pentagon and three triangles joining at a vertex.

This compound can be formed by inscribing six pentagonal antiprisms within an icosahedron (each by removing one pair of opposite vertices) and then rotating each antiprism by 36º around its axis.

Its quotient prismatic equivalent is the pentagonal antiprismatic hexateroorthowedge, which is eight-dimensional.

A double cover of this compound occurs as a special case of the great disnub dodecahedron.

Vertex coordinates
Coordinates for the vertices of a great snub dodecahedron of edge length 1 are given by all even permutations of:
 * $$\left(\pm\frac{5+2\sqrt5}{10},\,0,\,\pm\frac{3\sqrt5-5}{20}\right),$$
 * $$\left(\pm\frac{\sqrt5}{5},\,\pm\frac{1+\sqrt5}{4},\,\pm\frac{\sqrt5}{10}\right),$$
 * $$\left(\pm\frac{5+\sqrt5}{20},\,\pm\frac12,\,\pm\frac{5+\sqrt5}{10}\right).$$