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.

The small prismated hexeract contains the vertices and edges of the small rhombated penteractic prism, square-truncated tesseractic duoprism, truncated cubic-small rhombicuboctahedral duoprism, and octagonal-truncated cubic duoprismatic prism.

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