Great distetracontoctachoron

The great distetracontoctachoron, or giddic, is a nonconvex uniform polychoron that consists of 48 regular octahedra and 48 quasitruncated hexahedra. 2 octahedra and 8 quasitruncated hexahedra join at each vertex.

The great distetracontoctachoron contains the vertices of an octagrammic duoprism, sphenoverted tesseractitesseractihexadecachoron, and quasitruncated hexahedral prism.

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


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

The second set of vertices are identical to the vertices of an inscribed sphenoverted tesseractitesseractihexadecachoron.