Small cellated hexeract

The small cellated hexeract or scox, also called the stericated dodecapeton or stericated 6-cube, is a convex uniform polypeton. It consists of 12 small cellated penteracts, 64 rectified hexatera, 192 rectified pentachoric prisms, 240 square-octahedral duoprisms, and 160 triangular-cubic duoprisms. 2 small cellated penteracts, 1 rectified hexatera, 4 rectified pentachoric prisms, 6 square-octahedral duoprisms, and 4 triangular-cubic duoprisms join at each vertex. As the name suggests, it is the sterication of the hexeract.

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