Small cellidemihexeract

The small cellidemihexeract or sochax, also called the pentic 6-cube or stericated 6-demicube, is a convex uniform polypeton. It consists of 12 demipenteracts, 32 hexatera, 32 small cellidodecatera, 160 triangular-tetrahedral duoprisms, and 60 hexadecachoric prisms. 1 demipenteract, 1 hexateron, 5 small cellidodecatera, 10 triangular-tetrahedral duoprisms, and 5 hexadecachoric prisms join at each vertex. As the name suggests, it is the sterication of the demihexeract.

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

Representations
A small cellidemihexeract has the following Coxeter diagrams:
 * x3o3o *b3o3o3x (full symmetry)
 * s4o3o3o3o3x (as alternated small terated hexeract)
 * xx(xo)oo3ox(xo)xo3oo(oo)oo3ox(ox)oo3oo(ox)xx&#xt
 * x(xo)(ou)x3o(oo)(oo)o3o(xo)(xo)o3o(oo)(oo)o3x(ou)(xo)x&#xt