Tetracontoctarhombated tetracontoctachoron

The tetracontoctirhombated tetracontoctachoron, or croc, is a nonconvex uniform polychoron that consists of 48 great rhombicuboctahedra and 48 cuboctatruncated cuboctahedra. 2 of each join at each vertex.

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


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