Small skewverted ditrigonal prismatohexacosidishecatonicosachoron

The small skewverted ditrigonal prismatohexacosidishecatonicosachoron, or skiv datapixady, is a nonconvex uniform polychoron that consists of 720 decagrammic prisms, 600 cuboctahedra, 120 small rhombicosidodecahedra, and 120 great ditrigonal dodecicosidodecahedra. 1 cuboctahedron, 1 small rhombicosidodecahedron, 1 great ditrigonal dodecicosidodecahedron, and 2 decagrammic prisms join at each vertex.

Vertex coordinates
The vertices of a small skewverted ditrigonal prismatohexacosidishecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(0,\,±1,\,±(1+\sqrt5),\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+2\sqrt5}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±1,\,±1,\,±\frac{3+\sqrt5}{2},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac12,\,±\frac32\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{5-\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±1,\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{5+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±(2+\sqrt5),\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32,\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±3\frac{1+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{7+\sqrt5}{4},\,±(1+\sqrt5),\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±1,\,±(2+\sqrt5),\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{6+\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac32,\,±(1+\sqrt5),\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac32,\,±3\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{5+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac32,\,±\frac{5+2\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{1+2\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{1+3\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±(1+\sqrt5)\right).$$

Related polychora
The small skewverted ditrigonal prismatohexacosidishecatonicosachoron is the colonel of a regiment of 15 members, including three other Wythoffians, namely the small skewverted ditrigonal hexacositrishecatonicosachoron, small skewverted hexacositrishecatonicosachoron, and small skewverted dishexacosidishecatonicosachoron.