Distetracontoctachoron

The distetracontoctachoron, or doc, is a nonconvex uniform polychoron that consists of 48 great rhombicuboctahedra and 48 quasitruncated cuboctahedra. 2 of each join at each vertex.

Vertex coordinates
The vertices of a distetracontoctachoron of edge length 1 are given by all permutations of:


 * $$\left(±\frac{3+\sqrt2}{2},\,±\frac{2\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3-\sqrt2}{2},\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt2}{2},\,±\frac{2-\sqrt2}{2},\,±\sqrt2,\,±1\right).$$