Truncated icosahedral prism

The truncated icosahedral prism or tipe is a prismatic uniform polychoron that consists of 2 truncated icosahedra, 12 pentagonal prisms, and 20 hexagonal prisms. Each vertex joins 1 truncated icosahedron, 1 pentagonal prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated icosahedron. As such it is also a CRF segmentochoron (designated K-4.127 on Richard Klitzing's list).

Vertex coordinates
Coordinates for the vertices of a truncated icosahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:
 * $$\left(0,\,±\frac12,\,±3\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,±\frac12\right).$$

Representations
A truncated icosahedral prism has the following Coxeter diagrams:


 * x o5x3x (full symmetry)
 * oo5xx3xx&#x (bases considered separately)