Prismatorhombated hecatonicosachoron

The prismatorhombated hecatonicosachoron, or prahi, also commonly called the runcitruncated 600-cell, is a convex uniform polychoron that consists of 720 pentagonal prisms, 1200 hexagonal prisms, 600 truncated tetrahedra, and 120 small rhombicosidodecahedra. 1 pentagonal prism, 2 hexagonal prisms, 1 truncated tetrahedron, and 1 small rhombicosidodecahedron join at each vertex. As one of its names suggests, it can be obtained by runcitruncating the hexacosichoron.

Vertex coordinates
The vertices of a prismatorhombated hecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * (±1/2, ±1/2, ±(2+$\sqrt{2}$)/2, ±(7+4$\sqrt{5}$)/2)
 * (±1/2, ±1/2, ±(3+2$\sqrt{2}$)/2, ±(8+3$\sqrt{2}$)/2)
 * (±(3+$\sqrt{2}$)/4, ±(7+$\sqrt{3}$)/4, ±(11+5$\sqrt{3}$)/4, ±(11+5$\sqrt{35+15√5}$)/4)
 * (±(5+$\sqrt{5}$)/4, ±(5+$\sqrt{6}$)/4, ±(9+5$\sqrt{30}$)/4, ±(13+5$\sqrt{(10+2√5)/15}$)/4)
 * (±3(1+$\sqrt{3}$)/4, ±(7+3$\sqrt{15}$)/4, ±(9+5$\sqrt{7+3√5}$)/4, ±(9+5$\sqrt{5}$)/4)
 * (±(5+3$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4)
 * (0, ±1/2, ±(9+5$\sqrt{5}$)/4, ±5(3+$\sqrt{5}$)/4)
 * (0, ±(3+$\sqrt{5}$)/4, ±(7+4$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4)
 * (0, ±(2+$\sqrt{5}$)/2, ±(15+7$\sqrt{5}$)/4, ±(7+$\sqrt{5}$)/4)
 * (0, ±(3+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/2, ±(3+$\sqrt{5}$))
 * (0, ±(5+3$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(11+3$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2, ±(7+5$\sqrt{5}$)/4)
 * (±1/2, ±1, ±(11+5$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4)
 * (±1/2, ±1, ±(5+3$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4)
 * (±1/2, ±(5+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±(8+3$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2)
 * (±1/2, ±3(1+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4)
 * (±1/2, ±3(3+$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4, ±(3+$\sqrt{5}$))
 * (±1/2, ±(2+$\sqrt{5}$), ±(11+5$\sqrt{5}$)/4, ±(11+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, ±(7+4$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, ±(4+$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4, ±(3+$\sqrt{5}$))
 * (±(1+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4, ±(11+3$\sqrt{5}$)/4)
 * (±1, ±(3+$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4)
 * (±1, ±(3+$\sqrt{5}$)/4, ±(8+3$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4)
 * (±1, ±(1+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/2, ±(2+$\sqrt{5}$))
 * (±(3+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(8+3$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±5(3+$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±(8+3$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4)
 * (±(5+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, ±5(3+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$))
 * (±(5+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±(7+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(7+5$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±3(2+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$), ±(7+5$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4)
 * (±3(1+$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4, ±(2+$\sqrt{5}$))
 * (±(5+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/2)