Small prismated hexeract

The small prismated hexeract or spox, also called the runcinated dodecapeton or runcinated 6-cube, is a convex uniform polypeton. It consists of 12 small prismated penteracts, 64 dodecatera, 192 rectified pentachoric prisms, and 240 square-tetrahedral duoprisms. 3 small prismated penteracts, 1 dodecateron, 3 rectified pentachoric prisms, and 3 square-tetrahedral duoprisms join at each vertex. As the name suggests, it is the runcination of the hexeract.

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