Small rhombidemihexeract

The small rhombidemihexeract or sirhax, also called the runcic 6-cube or cantellated 6-demicube, is a convex uniform polypeton. It consists of 12 small rhombated demipenteracts, 32 dodecatera, and 32 small rhombated hexatera. 3 truncated small rhombated demipenteracts, 1 dodecateron, and 3 small rhombated hexatera join at each vertex. As the name suggests, it is the cantellation of the demihexeract.

Coordinates
The vertex coordinates of a small rhombidemihexeract, centered at the origin and with unit edge length, are given by all permutations and even sign changes of:
 * $$\left(\frac{3\sqrt8}{8},\,\frac{3\sqrt8}{8},\,\frac{3\sqrt8}{8},\,\frac{\sqrt8}{8},\,\frac{\sqrt8}{8},\,\frac{\sqrt8}{8}\right).$$

Representations
A small rhombidemihexeract has the following Coxeter diagrams:
 * x3o3o *b3x3o3o (full symmetry)
 * s4o3o3x3o3o (as alternated birectified hexacontatetrapeton)