Great disnub dishexacosichoron

The great disnub dishexacosichoron, or gadsadox, is a nonconvex uniform polychoron that consists of 4800 regular octahedra (falling in pairs into the same hyperplane, thus forming 2400 golden hexagrammic antiprisms) and 1200 regular great icosahedra (also falling in pairs in the same hyperplane, forming 600 small retrosnub disoctahedra). 8 octahedra and 4 great icosahedra join at each vertex.

This polychoron can be obtained as the blend of 10 rectified grand hexacosichora. In the process some of the octahedra blend out fully, while the other cells compound as noted above. In addition the vertex figure would in turn be a blend of two pentagrammic prismatic vertex figures of the rectified grand hexacosichoron.

Vertex coordinates
Coordinates for the vertices of a great disnub dishexacosichoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * $$\left(0,\,0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt{10}-2\sqrt2}{2}\right),$$
 * $$\left(±\frac{\sqrt2}{4},\,±\frac{\sqrt2}{4},\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{2\sqrt{10}-3\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{\sqrt{10}-\sqrt2}{8},\,±3\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{7\sqrt2-3\sqrt{10}}{8}\right),$$
 * $$\left(±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt2+\sqrt{10}}{8},\,±3\frac{3\sqrt2-\sqrt{10}}{8}\right),$$
 * $$\left(±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±\frac{3\sqrt2-\sqrt{10}}{4}\right),$$
 * $$\left(±\frac{5\sqrt2-\sqrt{10}}{8},\,±\frac{5\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{7\sqrt2-3\sqrt{10}}{8}\right),$$
 * $$\left(±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{\sqrt2}{4},\,±\frac{4\sqrt2-\sqrt{10}}{4}\right),$$
 * $$\left(±\frac{3\sqrt{10}-5\sqrt2}{8},\,±\frac{3\sqrt{10}-5\sqrt2}{8},\,±\frac{\sqrt2+\sqrt{10}}{8},\,±\frac{3\sqrt2-\sqrt{10}}{8}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{4},\,±\frac{5\sqrt2-\sqrt{10}}{8},\,±3\frac{3\sqrt2-\sqrt{10}}{8}\right),$$
 * $$\left(0,\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{2\sqrt{10}-3\sqrt2}{4},\,±\frac{5\sqrt2-\sqrt{10}}{8}\right),$$
 * $$\left(0,\,±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{3\sqrt{10}-5\sqrt2}{8},\,±\frac{4\sqrt2-\sqrt{10}}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±3\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{3\sqrt{10}-5\sqrt2}{8}\right),$$
 * $$\left(±\frac{\sqrt2+\sqrt{10}}{8},\,±\frac{\sqrt2}{4},\,±\frac{\sqrt{10}-\sqrt2}{2},\,±\frac{\sqrt{10}-\sqrt2}{8}\right),$$
 * $$\left(±\frac{\sqrt2+\sqrt{10}}{8},\,±\frac{\sqrt2}{4},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±\frac{7\sqrt2-3\sqrt{10}}{8}\right),$$
 * $$\left(±\frac{\sqrt2+\sqrt{10}}{8},\,±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{7\sqrt2-3\sqrt{10}}{8},\,±\frac{2\sqrt{10}-\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{4},\,±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{\sqrt{10}-\sqrt2}{4},\,±3\frac{3\sqrt2-\sqrt{10}}{8}\right),$$
 * $$\left(±\frac{\sqrt2}{4},\,±\frac{5\sqrt2-\sqrt{10}}{8},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±\frac{3\sqrt{10}-5\sqrt2}{8}\right),$$
 * $$\left(±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{2\sqrt{10}-3\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±\frac{4\sqrt2-\sqrt{10}}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{7\sqrt2-3\sqrt{10}}{8}\right),$$
 * $$\left(±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±3\frac{\sqrt{10}-\sqrt2}{8}\right),$$
 * $$\left(±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{5\sqrt2-\sqrt{10}}{8},\,±\frac{3\sqrt{10}-5\sqrt2}{8},\,±\frac{+\sqrt{10}-2\sqrt2}{4}\right).$$