Great rhombated hecatonicosachoron

The great rhombated hecatonicosachoron, or grahi, also commonly called the cantitruncated 120-cell, is a convex uniform polychoron that consists of 1200 triangular prisms, 600 truncated tetrahedra, and 120 great rhombicosidodecahedra. 1 triangular prism, 1 truncated tetrahedron, and 2 great rhombicosidodecahedra join at each vertex. As one of its names suggests, it can be obtained by cantitruncating the hecatonicosachoron.

Vertex coordinates
The vertices of a great rhombated hecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * (±1/2, ±1/2, ±(3+2$\sqrt{2}$)/2, ±5(2+$\sqrt{3}$)/2),
 * (±(5+3$\sqrt{(5+√5)/2}$)/4, ±3(3+$\sqrt{64+28√5}$)/4, ±(13+7$\sqrt{5}$)/4, ±(13+7$\sqrt{6}$)/4),
 * (±(7+3$\sqrt{30}$)/4, ±(7+3$\sqrt{3}$)/4, ±(11+7$\sqrt{15}$)/4, ±(15+7$\sqrt{7+3√5}$)/4),
 * (0, ±1/2, ±(19+7$\sqrt{5}$)/4, ±(13+7$\sqrt{5}$)/4),
 * (0, ±1/2, ±3(7+3$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4),
 * (0, ±(3+$\sqrt{5}$)/4, ±(9+4$\sqrt{5}$)/2, ±(11+7$\sqrt{5}$)/4),
 * (0, ±(3+$\sqrt{5}$)/4, ±(11+4$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4),
 * (0, ±(1+$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$), ±(5+3$\sqrt{5}$)/2),
 * (±1/2, ±(13+5$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2, ±5(3+$\sqrt{5}$)/4),
 * (±1/2, ±1, ±(17+7$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4),
 * (±1/2, ±(5+$\sqrt{5}$)/4, ±2(2+$\sqrt{5}$), ±(13+7$\sqrt{5}$)/4),
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±(11+4$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2),
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±5(2+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2),
 * (±1/2, ±3(1+$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$), ±(11+5$\sqrt{5}$)/4),
 * (±1/2, ±(7+3$\sqrt{5}$)/4, ±2(2+$\sqrt{5}$), ±5(3+$\sqrt{5}$)/4),
 * (±1, ±(3+$\sqrt{5}$)/4, ±5(2+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4),
 * (±1, ±(2+$\sqrt{5}$)/2, ±3(7+3$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4),
 * (±1, ±(3+$\sqrt{5}$)/2, ±2(2+$\sqrt{5}$), ±(7+3$\sqrt{5}$)/2),
 * (±1, ±(5+3$\sqrt{5}$)/4, ±(9+4$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4, ±(13+7$\sqrt{5}$)/4, ±5(3+$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±5(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4, ±(17+7$\sqrt{5}$)/4, ±5(3+$\sqrt{5}$)/4),
 * (±(1+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±5(2+$\sqrt{5}$)/2),
 * (±(1+$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2, ±(15+7$\sqrt{5}$)/4, ±5(3+$\sqrt{5}$)/4),
 * (±(5+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±3(7+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4),
 * (±(5+$\sqrt{5}$)/4, ±(4+$\sqrt{5}$)/2, ±(17+7$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2),
 * (±(5+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(19+7$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4),
 * (±(2+$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4, ±(11+7$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2),
 * (±(2+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/2, ±(13+7$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4),
 * (±3(1+$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4),
 * (±3(1+$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(13+7$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(11+4$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2, ±(15+7$\sqrt{5}$)/4, ±(13+7$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(19+7$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4),
 * (±(5+3$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4, ±(17+7$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4),
 * (±(4+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$), ±3(3+$\sqrt{5}$)/4),
 * (±(4+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(9+4$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2),
 * (±(7+3$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2, ±(17+7$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2),
 * (±(7+3$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4, ±2(2+$\sqrt{5}$), ±(5+2$\sqrt{5}$)/2),
 * (±(3+2$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4, ±2(2+$\sqrt{5}$)).