Quasitruncated penteract

The quasitruncated penteract, or quittin, also called the quasitruncated 5-cube, is a nonconvex uniform polyteron. It consists of 32 regular pentachora and 10 quasitruncated tesseracts. One pentachoron and 4 quasitruncated tesseracts join at each vertex. It is the quasitruncation of the penteract.

Vertex coordinates
The vertices of a quasitruncated penteract of edge length 1 are given by all permutations of:
 * $$\left(±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$$