Celligreatorhombated penteract

The celligreatorhombated penteract, or cogrin, also called the stericantitruncated 5-cube, is a convex uniform polyteron. It consists of 80 cuboctahedral prisms, 80 triangular-octagonal duoprisms, 40 great rhombicuboctahedral prisms, 10 great rhombated tesseracts, and 32 prismatorhombated pentachora. 1 prismatorhombated pentachoron, 1 cuboctahedral prism, 1 great rhombated tesseract, 1 triangular-octagonal duoprism, and 2 great rhombicuboctahedral prisms join at each vertex. As the name suggests, it is the stericantitruncation of the penteract.

Vertex coordinates
The vertices of a celligreatorhombated penteract of edge length 1 are given by all permutations of:
 * $$\left(\frac{1+3\sqrt2}{2},\,\frac{1+2\sqrt2}{2},\,\frac{1+2\sqrt2}{2},\,\frac{1+\sqrt2}{2},\,±\frac12\right).$$