Small hecatonicosiprismatodishecatonicosachoron

The small hecatonicosiprismatodishecatonicosachoron, or shipady, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 120 quasitruncated great stellated dodecahedra, 120 small icosicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 pentagrammic prism, 1 quasitruncated great stellated dodecahedron 1 small icosicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.

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

Related polychora
The small hecatonicosiprismatodishecatonicosachoron is the colonel of a 3-member regiment that also includes the small ditrigonal hecatonicosiprismatodishecatonicosachoron and small hecatonicosihecatonicosihecatonicosachoron.