Icositetraquasitruncated tetracontoctachoron

The icositetraquasitruncated tetracontoctachoron, or iquatoc, is a nonconvex uniform polychoron that consists of 24 truncated cubes, 24 quasitruncated hexahedra, and 24 cuboctatruncated cuboctahedra. 1 truncated cube, 1 quasitruncated hexahedron, and 2 cuboctatruncated cuboctahedra join at each vertex.

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


 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{\sqrt2-1}{2},\,±\frac32\right),$$
 * $$\left(±\frac{2+\sqrt2}{2},\,±1,\,±\frac{2-\sqrt2}{2},\,0\right).$$

The polychoron in dual F4 symmetry has vertices given by all permutations of:


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