Small prismatohecatonicosihexacosihecatonicosachoron

The small prismatohecatonicosihexacosihecatonicosachoron, or sphixhi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 600 truncated octahedra, 120 truncated great icosahedra, and 120 small icosicosidodecahedra. 1 triangular prism, 1 truncated great icosahedron, 1 small icosicosidodecahedron, and 2 truncated octahedra join at each vertex.

Vertex coordinates
The vertices of a small prismatohecatonicosihexacosihecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-1}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±1,\,±1,\,±\sqrt5,\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{1+2\sqrt5}{2},\,±\frac{1+2\sqrt5}{2},\,±\frac12,\,±\frac32\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{2},\,±(1+\sqrt5),\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{\sqrt5-1}{4},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{13+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{7-\sqrt5}{4},\,±\frac{1+2\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3\sqrt5-1}{4},\,±\frac{11+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-1}{4},\,±1,\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac{4+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±1,\,±\frac{9+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5}{2},\,±\frac32,\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3+\sqrt5}{4},\,±2,\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±2,\,±\frac{1+2\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{13+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{9+\sqrt5}{4},\,±\sqrt5\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac12,\,±\frac{7+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{11+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±5\frac{1+\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\sqrt5,\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{13+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{2\sqrt5-1}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±2,\,±\frac{9+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{9+\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±2,\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±1,\,±\frac{3+2\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac32,\,±\frac{9+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±2,\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±1,\,±\frac{4+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac32,\,±\frac{7+3\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{7-\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±1,\,±\frac32,\,±\frac{11+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\sqrt5,\,±3\frac{1+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\sqrt5,\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$

Related polychora
The small prismatohecatonicosihexacosihecatonicosachoron is the colonel of a 3-member regiment that also includes the small ditrigonal prismatotrishecatonicosachoron and small great hexacosidishecatonicosachoron.