Quasiprismatorhombated grand hexacosichoron

The quasiprismatorhombated grand hexacosichoron, or quippirgax, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 720 decagrammic prisms, 600 cuboctahedra, and 120 quasitruncated great stellated dodecahedra. 1 triangular prism, 2 decagrammic prisms, 1 cuboctahedron, and 1 quasitruncated great stellated dodecahedron join at each vertex. It can be obtained by quasiruncitruncating the great grand stellated hecatonicosachoron.

Vertex coordinates
The vertices of a quasiprismatorhombated grand hexacosichoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(0,\,±1,\,±\frac{7-3\sqrt5}{2},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±3\frac{\sqrt5-2}{2},\,±\frac{8-3\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{9-4\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{5-2\sqrt5}{2},\,±3\frac{\sqrt5-2}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{2},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{9\sqrt5-17}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(0,\,±\frac{5-\sqrt5}{4},\,±\frac{7\sqrt5-13}{4},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-2}{2},\,±\frac{19-7\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(0,\,±3\frac{\sqrt5-1}{4},\,±\frac{17-7\sqrt5}{4},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±(3-\sqrt5),\,±\frac{5\sqrt5-11}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{7\sqrt5-15}{4},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{19-7\sqrt5}{4},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{9\sqrt5-17}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{17-7\sqrt5}{4},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{9-4\sqrt5}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{2},\,±\frac{7\sqrt5-13}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-5}{4},\,±\frac{7\sqrt5-15}{4},\,±(3-\sqrt5)\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{9-4\sqrt5}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-2}{2},\,±\frac{7\sqrt5-15}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-9}{4},\,±3\frac{\sqrt5-2}{2},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{9\sqrt5-17}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{9-4\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{7-3\sqrt5}{2},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{8-3\sqrt5}{2},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{3\sqrt5-5}{2},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{9-4\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±3\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-2}{2},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±(\sqrt5-2),\,±\frac{7-3\sqrt5}{2},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{8-3\sqrt5}{2},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{5\sqrt5-9}{4},\,±\frac{3\sqrt5-5}{2},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{19-7\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{8-3\sqrt5}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±(\sqrt5-2),\,±3\frac{\sqrt5-2}{2},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{8-3\sqrt5}{2},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{5-2\sqrt5}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{17-7\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{7\sqrt5-15}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{5-2\sqrt5}{2},\,±(\sqrt5-2),\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{7-3\sqrt5}{4},\,±3\frac{\sqrt5-2}{2},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{7-3\sqrt5}{2},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{7\sqrt5-13}{4},\,±(\sqrt5-2)\right).$$

Related polychora
The quasiprismatorhombated grand hexacosichoron is the colonel of a 3-member regiment that also includes the great prismatohexacosihecatonicosihecatonicosachoron and the great rhombiprismic hexacosihecatonicosachoron.