Truncated icosahedron atop truncated dodecahedron

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:


 * (0, ±1/2, ±3(1+$\sqrt{2}$)/4, 1/2)
 * (±1/2, ±(5+$\sqrt{(5+√5)/2}$)/4, ±(1+$\sqrt{(5+√5)/2}$)/2, 1/2)
 * (±(1+$\sqrt{2}$)/4, ±1, ±(2+$\sqrt{5}$)/2, 1/2)
 * (0, ±1/2, ±(5+3$\sqrt{2}$)/4, 0)
 * (±1/2, ±(3+$\sqrt{3}$)/4, ±(3+$\sqrt{3}$)/2, 0)
 * (±(3+$\sqrt{8+3√5}$)/4, ±(1+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2, 0)