Truncated icosahedron atop truncated dodecahedron

The truncated icosahedron atop truncated dodecahedron, or tiatid, is a CRF segmentochoron (designated K-4.151 on Richard Klitzing's list). As the name suggests, it consists of a truncated icosahedron and a truncated dodecahedron as bases, connected by 30 tetrahedra, 20 triangular cupolas, and 12 pentagonal cupolas.

Vertex coordinates
The vertices of a truncated-icosahedron-atop-truncated-dodecahedron segmentochoron of edge length 1 are given by all even permutations of the first three coordinates of:


 * $$\left(0,\,±\frac12, ±3\frac{1+\sqrt5}{4},\,\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+3\sqrt5}{4},\,0\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,0\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,0\right).$$