Great icosicosidodecahedron

The great icosicosidodecahedron, or giid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 20 hexagons. One triangle, one pentagon, and two hexagons join at each vertex.

It is a faceting of the great ditrigonal dodecicosidodecahedron, using its 12 pentagons and 20 triangles along with 20 additional hexagons.

Vertex coordinates
The coordinates of a great icosicosidodecahedron with unit edge length are given by all sign changes and even permutations of:
 * $$\left(0,\,\frac{3-\sqrt5}{4},\,\frac{\sqrt5}{2}\right),$$
 * $$\left(\frac{3-\sqrt5}{4},\,\frac12,\,1\right),$$
 * $$\left(\frac12,\,\frac{\sqrt5-1}{2},\,\frac{1+\sqrt5}{4}\right).$$