Sphenoverted ditrigonal hexacosidishecatonicosachoron

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

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

Related polychora
The sphenoverted ditrigonal hexacosidishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the retrosphenoverted hecatonicosidishexacosichoron, great hecatonicosihexacosihecatonicosachoron, great retrohexacosidishecatonicosachoron, great dishecatonicosachoron, great hexacosihecatonicosintercepted hexacosihecatonicosachoron, and hecatonicosintercepted hexacosidishecatonicosachoron.