Antifrustary distetracontoctachoron

The antifrustary distetracontoctachoron, or afdec, is a nonconvex uniform polychoron that consists of 48 cuboctahedra and 48 great cubicuboctahedra. 2 cuboctahedra and 4 great cubicuboctahedra join at each vertex.

The antifrustary distetracontoctachoron contains the vertices of a hexagonal duoprism, small skewverted prismatohexadecadisoctachoron, octagonal-octagrammic duoprism, and cuboctatruncated cuboctahedral prism.

Vertex coordinates
Coordinates for the vertices of an antifrustary distetracontoctachoron of edge length 1 are all permutations of:


 * $$\left(±1,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac{\sqrt2-1}{2}\right).$$

The second set of vertices are identical to those of an inscribed small skewverted prismatohexadecadisoctachoron.

Related polychora
The antifrustary distetracontoctaachoron is the colonel of a regiment that conatins 53 uniform members, along with one fissary and one compound. 7 uniform members, plus the fissary and compound, have fullsymmetry, while the other facetings have single F4 symmetry only.