Icosidodecatruncated icosidodecahedron

The icosidodecatruncated icosidodecahedron or idtid, also called the icositruncated dodecadodecahedron, is a uniform polyhedron. It consists of 12 decagrams, 12 decagons, and 20 hexagons, with one of each type of face meeting per vertex.

It can be alternated into the snub icosidodecadodecahedron after equalizing edge lengths.

Vertex coordinates
An icosidodecatruncated icosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4}\right).$$