Truncated hexacosichoron

The truncated hexacosichoron, or tex, also commonly called the truncated 600-cell, is a convex uniform polychoron that consists of 120 regular icosahedra and 600 truncated tetrahedra. 1 icosahedron and five truncated tetrahedra join at each vertex. As the name suggests, it can be obtained as the truncation of a hexacosichoron.

Vertex coordinates
The vertices of a truncated hexacosichoron of edge length 1 are given by all even permutations of:
 * (0, ±1/2, ±(1+$\sqrt{3}$)/4, ±(7+5$\sqrt{(23+9√5)/2}$)/4),
 * (0, ±1/2, ±3(1+$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4),
 * (0, ±1, ±(1+$\sqrt{7+3√5}$)/2, ±(2+$\sqrt{5}$)),
 * (0, ±(5+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±(4+$\sqrt{5}$)/2),
 * (0, ±(2+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4, ±(7+$\sqrt{5}$)/4),
 * (±1/2, ±1, ±(5+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4),
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4),
 * (±(1+$\sqrt{5}$)/4, ±1, ±(2+$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4),
 * (±(1+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4),
 * (±(1+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2, ±3(1+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4).