Great rhombated hexacosichoron

The great rhombated hexacosichoron, or grix, also commonly called the cantitruncated 600-cell, is a convex uniform polychoron that consists of 720 pentagonal prisms, 600 truncated octahedra, and 120 truncated icosahedra. 1 penatgonal prism, 1 truncated icosahedron, and 2 truncated octahedra join at each vertex. As one of its names suggests, it can be obtained by cantitruncating the hexacoscichoron.

Vertex coordinates
The vertices of a great rhombated tesseract of edge length 1 are given by all permutations of: Plus all even permutations of:
 * (±1/2, ±1/2, ±(4+3$\sqrt{2}$)/2, ±(8+3$\sqrt{5}$)/2)
 * (±1/2, ±3/2, ±3(2+$\sqrt{3}$)/2, ±3(2+$\sqrt{43+18√5}$)/2)
 * (±1, ±1, ±(5+3$\sqrt{5}$)/2, ±(7+3$\sqrt{(5+2√5)/10}$)/2)
 * (0, ±1/2, ±3(1+$\sqrt{3}$)/4, ±3(5+3$\sqrt{7+3√5}$)/4)
 * (0, ±1/2, ±5(1+$\sqrt{5}$)/4, ±(17+7$\sqrt{5}$)/4)
 * (0, ±1, ±(1+$\sqrt{5}$), ±2(2+$\sqrt{5}$))
 * (0, ±(11+3$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4, ±(7+2$\sqrt{5}$)/2)
 * (0, ±(5+2$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4, ±(13+3$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/2, ±(7+5$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±3(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±1/2, ±(7+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±2(2+$\sqrt{5}$))
 * (±1/2, ±3(1+$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4)
 * (±1/2, ±(4+$\sqrt{5}$)/2, ±3(2+$\sqrt{5}$)/2, ±(7+2$\sqrt{5}$)/2)
 * (±1/2, ±(7+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2, ±(13+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, ±1, ±(2+$\sqrt{5}$)/2, ±3(5+3$\sqrt{5}$)/4)
 * (±·1+$\sqrt{5}$)/4, ±3/2, ±(5+3$\sqrt{5}$)/4, ±2(2+$\sqrt{5}$))
 * (±(1+$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2, ±(7+2$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$), ±3(2+$\sqrt{5}$)/2, ±(13+3$\sqrt{5}$)/4)
 * (±1, ±(1+$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$))
 * (±1, ±(7+$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4)
 * (±1, ±3(1+$\sqrt{5}$)/4, ±(17+7$\sqrt{5}$)/4, ±(4+$\sqrt{5}$)/2)
 * (±1, ±(5+3$\sqrt{5}$)/4, ±(8+3$\sqrt{5}$)/2, ±(11+3$\sqrt{5}$)/4)
 * (±3/2, ±(1+$\sqrt{5}$)/2, ±(17+7$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±3/2, ±(5+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4)
 * (±3/2, ±(2+$\sqrt{5}$)/2, ±(8+3$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4, ±(4+3$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(11+3$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2)
 * (±(5+$\sqrt{5}$)/4, ±(7+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2, ±3(2+$\sqrt{5}$)/2)
 * (±(5+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2)
 * (±(5+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$), ±(8+3$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±(7+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2, ±(4+3$\sqrt{5}$)/2, ±3(2+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4, ±5(1+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2)
 * (±(7+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(8+3$\sqrt{5}$)/2, ±(2+$\sqrt{5}$))
 * (±3(1+$\sqrt{5}$)/4, ±(4+$\sqrt{5}$)/2, ±(7+5$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2)
 * (±3(1+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$), ±(4+3$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4)
 * (±3(1+$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2)
 * (±(5+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(4+3$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/2)
 * (±(5+3$\sqrt{5}$)/4, ±5(1+$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$))
 * (±(1+$\sqrt{5}$), ±(7+3$\sqrt{5}$)/4, ±(7+5$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2)