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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{7+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{9+5\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right).$$

Semi-uniform variant
The small disprismatohexacosihecatonicosachoron has a semi-uniform variant of the form x5o3o3y that maintains its full symmetry. This variant uses 120 dodecahedra of size x, 600 tetrahedra of size y, 1200 semi-uniform triangular prisms of form x y3o, and 720 semi-uniform pentagonal prisms of form y x5o as cells, with 2 edge lengths.

With edges of length a (of dodecahedra) and b (of tetrahedra), its circumradius is given by $$\sqrt{\frac{14a^2+3b^2+11ab+(6a^2+b^2+5ab)\sqrt5}{2}}$$.

Related polychora
The small disprismatohexacosihecatonicosachoron is the colonel of a 7-member regiment.

Sidpixhi regiment The segmentochoron dodecahedron atop small rhombicosidodecahedron can be obtained as a cap of the small disprismatohexacosihecatonicosachoron. Another segmentochoral cap is the pentagonal cupofastegium.