Great rhombated hexeract

The great rhombated hexeract or grox, also called the cantitruncated dodecapeton or cantitruncated 6-cube, is a convex uniform polypeton. It consists of 12 great rhombated penteracts, 64 truncated hexatera, and 192 pentachoric prisms. 4 great rhombated penteracts, 1 truncated hexateron, and 1 pentachoric prism join at each vertex. As the name suggests, it is the cantitruncation of the hexeract.

Coordinates
The vertex coordinates of a great rhombated hexeract, centered at the origin and with unit edge length, are given by all permutations of:
 * $$\left(±\frac{1+2\sqrt2}{2},\,±\frac{1+2\sqrt2}{2},\,±\frac{1+2\sqrt2}{2},\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$