Great sphenoverted hexacosidishecatonicosachoron

The great sphenoverted hexacosidishecatonicosachoron, or gwavixady, is a nonconvex uniform polychoron that consists of 600 regular octahedra, 120 quasitruncated great stellated dodecahedra, and 120 great dodecicosidodecahedra. 1 octahedron, 2 quasitruncated great stellated dodecahedra, and 2 great dodecicosidodecahedra join at each vertex.

Vertex coordinates
Coordinates for the vertices of a great sphenoverted hexacosidishecatonicosachoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * $$\left(0,\,0,\,±(\sqrt5-2),\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{5-2\sqrt5}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{2},\,±(\sqrt5-2),\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{13-5\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac{5\sqrt5-11}{4},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-2}{2},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-2}{2},\,±\frac{5\sqrt5-9}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-9}{4},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{13-5\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{5\sqrt5-11}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7-3\sqrt5}{4},\,±(\sqrt5-2),\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{5-2\sqrt5}{2},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{13-5\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±(3-\sqrt5),\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{5\sqrt5-11}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{5\sqrt5-9}{4}\right).$$

Related polychora
The great sphenoverted hexacosidishecatonicosachoron is the colonel of a seven-member regiment. Its other members include the quasirhombated great grand stellated hecatonicosachoron, great rhombic dishecatonicosachoron, great pseudorhombic prismatohecatonicosachoron, grand quasirhombic prismatohecatonicosachoron, disprismatointercepted hexacosihecatonicosachoron, and prismatointercepted hexacosidishecatonicosachoron.