Prismatorhombidemihexeract

The prismatorhombidemihexeract or prohax, also called the steriruncic 6-cube or runcicantellated 6-demicube, is a convex uniform polypeton. It consists of 12 prismatorhombated demipenteracts, 32 bitruncated hexatera, 32 prismatorhombated hexatera, and 160 triangular-tetrahedral duoprisms. 2 prismatorhombated demipenteracts, 1 bitruncated hexateron, 3 prismatorhombated hexatera, and 1 triangular-tetrahedral duoprism join at each vertex. As the name suggests, it is the runcicantellation of the demihexeract.

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

Representations
A prismatorhombidemihexeract has the following Coxeter diagrams:
 * x3o3o *b3x3x3o (full symmetry)
 * s4o3o3x3x3o (as alternated bitruncated hexacontatetrapeton)