Prismatorhombated hexacosichoron

The prismatorhombated hexacosichoron, or prix, also commonly called the runcitruncated 120-cell, is a convex uniform polychoron that consists of 1200 triangular prisms, 720 decagonal prisms, 600 cuboctahedra, and 120 truncated dodecahedra. 1 triangular prism, 2 decagonal prisms, 1 cuboctahedron, and 1 truncated dodecahedron join at each vertex. As one of its names suggests, it can be obtained by runcitruncating the hecatonicosachoron.

Vertex coordinates
The vertices of a prismatorhombated hexacosichoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * (0, ±1, ±(7+3$\sqrt{2}$)/2, ±(7+3$\sqrt{2}$)/2)
 * (±1/2, ±1/2, ±3(2+$\sqrt{2}$)/2, ±(8+3$\sqrt{2}$)/2)
 * (±1/2, ±1/2, ±(3+2$\sqrt{(5+√5)/2}$)/2, ±(9+4$\sqrt{(5+√5)/2}$)/2)
 * (±(2+$\sqrt{48+21√5}$)/2, ±(5+2$\sqrt{5}$)/2, ±3(2+$\sqrt{6}$)/2, ±3(2+$\sqrt{30}$)/2)
 * (±(3+$\sqrt{(10+2√5)/15}$)/2, ±(3+$\sqrt{(5+2√5)/10}$)/2, ±(5+3$\sqrt{7+3√5}$)/2, ±(7+3$\sqrt{5}$)/2)
 * (0, ±1/2, ±(17+9$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4)
 * (0, ±(5+$\sqrt{5}$)/4, ±(13+7$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2)
 * (0, ±(2+$\sqrt{5}$)/2, ±(19+7$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4)
 * (0, ±3(1+$\sqrt{5}$)/4, ±(17+7$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2)
 * (±1/2, ±(3+$\sqrt{5}$), ±(11+5$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4)
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2)
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±(19+7$\sqrt{5}$)/4, ±(2+$\sqrt{5}$))
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±(17+9$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±(17+7$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±(9+4$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2)
 * (±1/2, ±(3+$\sqrt{5}$)/2, ±(13+7$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4)
 * (±1/2, ±(5+3$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4, ±(3+$\sqrt{5}$))
 * (±1, ±(3+$\sqrt{5}$)/4, ±(9+4$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4)
 * (±1, ±(2+$\sqrt{5}$)/2, ±(15+7$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$))
 * (±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, ±(17+9$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(9+4$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(8+3$\sqrt{5}$)/2, ±(3+$\sqrt{5}$))
 * (±(3+$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±(9+4$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$), ±(7+3$\sqrt{5}$)/2, ±(3+$\sqrt{5}$))
 * (±(5+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±(8+3$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(19+7$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(8+3$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2)
 * (±3(1+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$), ±3(2+$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(8+3$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4, ±(17+7$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(15+7$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4)
 * (±(5+3$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(2+$\sqrt{5}$), ±(15+7$\sqrt{5}$)/4)
 * (±(5+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/2)
 * (±(5+3$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4)
 * (±(7+3$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2, ±(13+7$\sqrt{5}$)/4, ±(2+$\sqrt{5}$))

Related polychora
The segmentochoron truncated dodecahedron atop great rhombicosidodecahedron can be obtained as a cap of the prismatorhombated hexacosichoron.