Small disprismatohexacosihecatonicosachoron

The small disprismatohexacosihecatonicosachoron, or sidpixhi, also commonly called the runcinated 120-cell, is a convex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, 1200 triangular prisms, and 720 pentagonal prisms. 1 tetrahedron, 1 dodecahedron, 3 triangular prisms, and 3 pentagonal prisms join at each vertex. It is the result of expanding the cells of either a hecatonicosachoron or a hexacosichoron outwards, and thus could also be called the runcinated 600-cell.

Vertex coordinates
The vertices of a small disprismatohexacosihecatonicosachoron of edge length 1 are all permutations of: along with the even permutations of:
 * (±1/2, ±1/2, ±(3+$\sqrt{5}$)/2, ±(5+2$\sqrt{2}$)/2)
 * (±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{6}$)/4, ±(9+5$\sqrt{30}$)/4)
 * (±(1+$\sqrt{(10+2√5)/15}$)/4, ±(5+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2)
 * (0, ±1/2, ±(7+3$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4)
 * (0, ±1/2, ±(9+5$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4)
 * (0, ±(1+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$), ±(3+$\sqrt{5}$)/2)
 * (0, ±(3+$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4)
 * (0, ±(3+$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$), ±(5+3$\sqrt{5}$)/4)
 * (±1/2, ±(3+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$))
 * (±(1+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4)

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