Small disnub dishexacosichoron

The small disnub dishexacosichoron, or sadsadox, 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 icosahedra (also falling in pairs in the same hyperplane, forming 600 snub disoctahedra). 8 octahedra and 4 icosahedra join at each vertex.

This polychoron can be obtained as the blend of 10 rectified hexacosichora, positioned in a similar way to the compound of 10 hexacosichora known as the snub decahecatonicosachoron. 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 pentagonal prismatic vertex figures of the rectified hexacosichoron.

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

Related polychora
The regiment of the small disnub dishexacosichoron, known as the "sidtaps", contains 9 uniform members, 11 scaliform members, 3 fissary scaliforms, and a number of uniform compounds.