Truncated hecatonicosachoron

The truncated hecatonicosachoron, or thi, also commonly called the truncated 120-cell, is a convex uniform polychoron that consists of 600 regular tetrahedra and 120 truncated dodecahedra. 1 tetrahedron and three truncated dodecahedra join at each vertex. As the name suggests, it can be obtained by truncating the hecatonicosachoron.

Vertex coordinates
The vertices of a truncated hecatonicosachoron of edge length 1 are given by all permutations of: along with all even permutations of:
 * $$\left(±\frac12,\,±\frac{5+2\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{8+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5){2},\,±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{7+3\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{13+5\sqrt5}{2},\,±\frac{11+5\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{15+7\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±3\frac2+\sqrt5}{2},\,±\frac{9+5\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{8+3\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{7+3\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{15+7\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±3\frac{2+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{15+7\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{13+5\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±{3+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{9+5\sqrt5}{4},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{11+5\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{11+5\sqrt5}{2},\,±\frac{9+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{2+\sqrt5){2},\,±\frac{5+3\sqrt5}{4},\,±\frac{13+5\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right).$$