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 convex 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:
 * (0, ±1/2, ±3(1+$\sqrt{5}$)/4, ±1/2),
 * (±1/2, ±(5+$\sqrt{3}$)/4, ±(1+$\sqrt{3}$)/2, ±1/2),
 * (±(1+$\sqrt{2}$)/4, ±1, ±(2+$\sqrt{(31+9√5)/8}$)/2, ±1/2).

Representations
A truncated icosahedral prism has the following Coxeter diagrams:


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