Truncated hecatonicosachoric prism

The truncated hecatonicosachoric prism or thipe is a prismatic uniform polyteron that consists of 2 truncated hecatonicosachora, 120 truncated dodecahedral prisms, and 600 tetrahedral prisms. 1 truncated hecatonicosachoron, 1 tetrahedral prism, and 3 truncated dodecahedral prisms join at each vertex. As the name suggests, it is a prism based on the truncated hecatonicosachoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a truncated hecatonicosachoric prism of edge length 1 are given by all permutations of the first four coordinates of: along with all even permutations of the first four coordinates of:
 * $$\left(±\frac12,\,±\frac{5+2\sqrt5}2,\,±\frac{5+2\sqrt5}2,\,±\frac{5+2\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}2,\,±\frac{2+\sqrt5}2,\,±\frac{2+\sqrt5}2,\,±\frac{8+3\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}2,\,±\frac{3+\sqrt5}2,\,±\frac{3+\sqrt5}2,\,±\frac{7+3\sqrt5}2,\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{13+5\sqrt5}2,\,±\frac{11+5\sqrt5}2,\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{15+7\sqrt5}4,\,±\frac{5+3\sqrt5}4,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}4,\,±3\frac{2+\sqrt5}2,\,±\frac{9+5\sqrt5}4,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}4,\,±\frac{8+3\sqrt5}2,\,±\frac{7+3\sqrt5}4,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{7+3\sqrt5}2,\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{15+7\sqrt5}4,\,±\frac{3+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}2,\,±3\frac{2+\sqrt5}2,\,±\frac{5+2\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{15+7\sqrt5}4,\,±\frac{2+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2,\,±\frac{13+5\sqrt5}2,\,±\frac{5+2\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}4,\,±(2+\sqrt5),\,±\frac{9+5\sqrt5}4,\,±\frac{5+2\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}2,\,±\frac{7+3\sqrt5}4,\,±\frac{11+5\sqrt5}2,\,±\frac{5+2\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}2,\,±\frac{3+\sqrt5}2,\,±\frac{11+5\sqrt5}2,\,±\frac{9+5\sqrt5}4,\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{13+5\sqrt5}2,\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±3\frac{2+\sqrt5}2,\,±\frac{7+3\sqrt5}4,\,±\frac12\right).$$