Hexacosihecatonicosachoron

The hexacosihecatonicosachoron, or xhi, also commonly called the bitruncated 120-cell, is a convex uniform polychoron that consists of 600 truncated tetrahedra and 120 truncated icosahedra. 2 trunctaed tetrahedra and 2 truncated icosahedra join at each vertex. It is the medial stage of the truncation series between a hecatonicosachoron and its dual hexacosichoron. As such is could also be called a bitruncated 600-cell.

Vertex coordinates
The vertices of a hexacosihecatonicosachoron of edge length 1 are all permutations of: Plus all even permutations of:
 * (0, 0, ±(1+$\sqrt{5}$), ±(7+3$\sqrt{3}$)/2)
 * (±(5+$\sqrt{(59+25√5)/2}$)/4, ±(5+$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4, ±(9+5$\sqrt{7+3√5}$)/4)
 * (0, ±1/2, ±(13+5$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4)
 * (0, ±1/2, ±3(1+$\sqrt{5}$)/4, ±(13+7$\sqrt{5}$)/4)
 * (0,±(1+$\sqrt{5}$)/4 ±5(3+$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2)
 * (0, ±3(3+$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(11+3$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±(13+7$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±5(3+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±1/2, ±1, ±(11+5$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4)
 * (±1/2, ±(3+$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4, ±(11+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, ±1, ±(2+$\sqrt{5}$)/2, ±(13+7$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4, ±(11+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2)
 * (±1, ±(1+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2)
 * (±1, ±(2+$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4)
 * (±1, ±(5+$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$), ±(11+5$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(7+5$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4)
 * (±3(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4)
 * (±(5+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, ±5(3+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±(5+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)