Prismatotruncated hexeract

The prismatotruncated hexeract or potax, also called the runcitruncated dodecapeton or runcitruncated 6-cube, is a convex uniform polypeton. It consists of 12 prismatotruncated penteracts, 64 small rhombated hexatera, 192 rectified pentachoric prisms, and 240 octagonal-tetrahedral duoprisms. 3 prismatotruncated penteracts, 1 small rhombated hexateron, 1 rectified pentachoric prism, and 2 octagonal-tetrahedral duoprisms join at each vertex. As the name suggests, it is the runcitruncation of the hexeract.

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