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. Its other members include the small hecatonicosafaceted prismatohecatonicosihexacosichoron, small hexacosifaceted prismatodishecatonicosachoron, small hexacosihecatonicosihecatonicosachoron, prismatoprismatohecatonicosachoron, smal spinoprismatohexacosihecatonicosachoron, and small spinoprismatodishecatonicoosachoron.

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