Great prismatohexacosidishecatonicosachoron

The great prismatohexacosidishecatonicosachoron, or gippixady, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 600 truncated tetrahedra, 120 great dodecicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 pentagrammic prism, 1 truncated tetrahedron, 1 great dodecicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates
The vertices of a great prismatohexacosidishecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{4\sqrt5-7}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{8-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{5\sqrt5-11}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{5\sqrt5-9}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{5\sqrt5-9}{4},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{5\sqrt5-7}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5\sqrt5-9}{4},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{4\sqrt5-7}{2},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-2}{2},\,±\frac{7\sqrt5-15}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{2},\,±(3-\sqrt5)\right),$$
 * $$\left(0,\,±\frac{3\sqrt5-5}{4},\,±3\frac{\sqrt5-2}{2},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{2},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{5\sqrt5-11}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{3\sqrt5-5}{4},\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{2},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{8-3\sqrt5}{2},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±3\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{2},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±3\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-9}{4},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac12,\,±(\sqrt5-2),\,±\frac{5\sqrt5-11}{4},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{4\sqrt5-7}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{5\sqrt5-11}{4},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{13-5\sqrt5}{4},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-2}{2},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{8-3\sqrt5}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-1}{2},\,±\frac{7-3\sqrt5}{2},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{8-3\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±5\frac{3-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-7}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{8-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{5\sqrt5-9}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{13-5\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±5\frac{3-\sqrt5}{4},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{7-3\sqrt5}{2},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{2},\,±\frac{5\sqrt5-7}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±(\sqrt5-2),\,±\frac{5\sqrt5-7}{4},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{5\sqrt5-11}{4},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{3\sqrt5-5}{2}\right).$$

Related polychora
The great prismatohexacosidishecatonicosachoron is the colonel of a 3-member regiment that also includes the prismatoquasirhombated great grand stellated hecatonicosachoron and great rhombiprismic dishecatonicosachoron.