Great quasirhombated penteract

The great quasirhombated penteract, or gaqrin, is a nonconvex uniform polyteron. It consists of 80 tetrahedral prisms, 32 truncated pentachora, and 10 great quasirhombated tesseracts. One truncated pentachoron, 1 tetrahedral prism, and 3 great quasirhombated tesseracts join at each vertex. It is the quasicantitruncation of the penteract.

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