Great rhombated penteract

The great rhombated penteract, or girn, also called the cantitruncated 5-cube, is a convex uniform polyteron. It consists of 80 tetrahedral prisms, 32 truncated pentachora, and 10 great rhombated tesseracts. One truncated pentachoron, 1 tetrahedral prism, and 3 great rhombated tesseracts join at each vertex. As the name suggests, it is the cantitruncation of the penteract.

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