Great hexacosihecatonicosachoron

The great hexacosihecatonicosachoron, or gixhi, is a nonconvex uniform polychoron that consists of 600 truncated tetrahedra and 120 truncated great icosahedra. 2 of each join at each vertex.

It is the medial stage of the truncation series between a great grand stellated hecatonicosachoron and its dual grand hexacosichoron, which makes it the bitruncation of either of these polychora.

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