Great rhombidemihexeract

The great rhombidemihexeract or girhax, also called the runcicantic 6-cube or cantitruncated 6-demicube, is a convex uniform polypeton. It consists of 12 great rhombated demipenteracts, 32 bitruncated hexatera, and 32 great rhombated hexatera. 3 great rhombated demipenteracts, 1 bitruncated hexateron, and 2 great rhombated hexatera join at each vertex. As the name suggests, it is the cantitruncation of the demihexeract.

Coordinates
The vertex coordinates of a great rhombidemihexeract, centered at the origin and with unit edge length, are given by all permutations and even sign changes of:
 * $$\left(\frac{5\sqrt8}{8},\,\frac{5\sqrt8}{8},\,\frac{5\sqrt8}{8},\,\frac{3\sqrt8}{8},\,\frac{\sqrt8}{8},\,\frac{\sqrt8}{8}\right).$$

Representations
A great rhombidemihexeract has the following Coxeter diagrams:
 * x3x3o *b3x3o3o (full symmetry)
 * s4o3x3x3o3o (as alternated hexeractihexacontatetrapeton)