Small skewverted prismatotrishecatonicosachoron

The small skewverted prismatotrishecatonicosachoron, or sik vipathi, is a nonconvex uniform polychoron that consists of 720 decagrammic prisms, 120 small rhombicosidodecahedra, 120 rhombidodecadodecahedra, and 120 great dodecicosidodecahedra. 1 small rhombicosidodecahedron, 1 rhombidodecadodecahedron, 1 great dodecicosidodecahedron, and 2 decagrammic prisms join at each vertex.

Vertex coordinates
The vertices of a small skewverted prismatotrishecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5}{2},\,±\frac52\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-1}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac52\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{2},\,±1,\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±1,\,±\frac{1+3\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±3\frac{\sqrt5-1}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{1+3\sqrt5}{4},\,±2\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±2,\,±\frac32\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±\frac52,\,±1\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac12,\,±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±2\right),$$
 * $$\left(±\frac12,\,±3\frac{\sqrt5-1}{4},\,±3\frac{1+\sqrt5}{4},\,±1\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{7+\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±2\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±1,\,±\frac{1+\sqrt5}{2},\,±2\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±1,\,±\frac{3\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±2,\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4}\right).$$

Related polychora
The small skewverted prismatotrishecatonicosachoron is the colonel of a regiment of 15 members, including three other Wythoffians, namely the skewverted tetrishecatonicosachoron, great skewverted prismatotrishecatonicosachoron, and skewverted prismatotrishecatonicosachoron.