Icositetraquasitruncated prismatotetracontoctachoron

The icositetraquasitruncated prismatotetracontoctachoron, or iquatpic, is a nonconvex uniform polychoron that consists of 96 hexagonal prisms, 24 great rhombicuboctahedra, 24 quasitruncated cuboctahedra, and 24 cuboctatruncated cuboctahedra. 1 of each type of cell join at each vertex.

Vertex coordinates
The vertices of an icositetraquasitruncated prismatotetracontoctachoron of edge length 1 are given by all permutations of:


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