Small rhombated hecatonicosachoron

The small rhombated hecatonicoscahoron, or srahi, also commonly called the cantellated 120-cell, is a convex uniform polychoron that consists of 600 regular octahedra, 1200 triangular prisms, and 120 small rhombicosidodecahedra. 1 octahedron, 2 triangular prisms, and 2 small rhombicosidodecahedra join at each vertex. As one of its names suggests, it can be obtained by cantellating the hecatonicosachoron.

Vertex coordinates
Coordinates for the vertices of a small rhombated hecatonicosachoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * (0, 0, ±(2+$\sqrt{2}$), ±(3+$\sqrt{5}$)),
 * (±1/2, ±1/2, ±(2+$\sqrt{23+10√5}$)/2, ±3(2+$\sqrt{5}$)/2),
 * (±1/2, ±1/2, ±(5+2$\sqrt{6}$)/2, ±(5+2$\sqrt{30}$)/2),
 * (±(1+$\sqrt{3}$)/2, ±(3+$\sqrt{15}$)/2, ±(2+$\sqrt{7+3√5}$), ±(2+$\sqrt{5}$)),
 * (±(2+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2),
 * (0, ±1/2, ±(13+5$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4),
 * (0, ±(1+$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2),
 * (0, ±(3+$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4),
 * (0, ±(2+$\sqrt{5}$)/2, ±(9+5$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4),
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)),
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2),
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4),
 * (±1/2, ±(7+3$\sqrt{5}$)/4, ±(2+$\sqrt{5}$), ±3(3+$\sqrt{5}$)/4),
 * (±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, ±3(2+$\sqrt{5}$)/2),
 * (±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)),
 * (±(3+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$), ±(7+3$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)),
 * (±·1+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4),
 * (±(5+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2),
 * (±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(9+5$\sqrt{5}$)/4).

Related polychora
The segmentochoron small rhombicosidodecahedron atop truncated dodecahedron can be obtained as a cap of the small rhombated hecatonicosachoron.