Truncated great dodecahedron

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

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