Sphenoverted hecatonicosidishexacosichoron

The sphenoverted hecatonicosidishexacosichoron, or wavhiddix, is a nonconvex uniform polychoron that consists of 600 regular octahedra, 600 truncated tetrahedra, and 120 small icosicosidodecahedra. 1 octahedron, 2 truncated tetrahedra, and 2 small icosicosidodecahedra join at each vertex.

A semi-uniform variant of this polychoron can be constructed as a rectified small ditetrahedronary hexacosihecatonicosachoron.

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

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