Truncated great icosahedron

The truncated great icosahedron, or tiggy, also called the great truncated icosahedron, is a uniform polyhedron. It consists of 12 pentagrams and 20 hexagons. Each vertex joins one pentagram and two hexagons. As the name suggests, it can be obtained by the truncation of the great icosahedron.

Vertex coordinates
A truncated great icosahedron of edge length 1 has vertex coordinates given by all even permutations and all changes of sign of:
 * $$\left(0,\,±\frac12,\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{\sqrt5-2}{2}\right).$$