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:
 * (±1/2, ±(5+2$\sqrt{(5+√5)/2}$)/2, ±(5+2$\sqrt{34+15√5}$)/2, ±(5+2$\sqrt{5}$)/2),
 * (±(2+$\sqrt{7+3√5}$)/2, ±(2+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2, ±(8+3$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/2).
 * (0, ±1/2, ±(13+5$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/2),
 * (0, ±1/2, ±(15+7$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4),
 * (0, ±(3+$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4),
 * (0, ±(3+$\sqrt{5}$)/4, ±(8+3$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4),
 * (0,±(1+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)),
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2),
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±3(2+$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, ±(15+7$\sqrt{5}$)/4, ±·2+$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$), ±(9+5$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2),
 * (±(1+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2),
 * (±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4),
 * (±(2+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)),
 * (±(3+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4.