Prismatorhombated hexeract

The prismatorhombated hexeract or prox, also called the runcicantellated dodecapeton or runcicantellated 6-cube, is a convex uniform polypeton. 3 prismatorhombated penteracts, 1 bitruncated hexateron, 2 truncated pentachoric prisms, and 1 square-tetrahedral duoprisms join at each vertex. As the name suggests, it is the runcicantellation of the hexeract.

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