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 and edges 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.

Related polychora
The great distetracontoctachoron is the colonel of a regiment that includes 20 members, 2 fissaries, and a compound. Among the members, 8 in total have doubled F4 symmetry, including the great distetracontoctachoron itself, the quasiprismatotetracontoctachoron, and the noble great retrotetracontoctachoron, while the 12 remaining members, and the fissaries and compound, have single F4 symmetry only.