Cellirhombated hexeract

The cellirhombated hexeract or crax, also called the stericantellated dodecapeton or stericantellated 6-cube, is a convex uniform polypeton. It consists of 12 cellirhombated penteracts, 64 small birhombidodecatera, 192 small rhombated pentachoric prisms, 240 square-octahedral duoprisms, and 160 triangular-small rhombicuboctahedral duoprisms. 2 cellirhombated penteracts, 1 small birhombidodecatera, 2 small rhombated pentachoric prisms, 1 square-octahedral duoprism, and 2 triangular-small rhombicuboctahedral duoprisms join at each vertex. As the name suggests, it is the stericantellation of the hexeract.

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