Small biprismated hexeract

The small biprismated hexeract or sobpoxog, also called the biruncinated dodecapeton or biruncinated 6-cube, is a convex uniform polypeton. It consists of 12 small prismated triacontaditera, 64 small prismated hexatera, 240 square-octahedral duoprisms, and 160 triangular-cuboctahedral duoprisms. 2 small prismated triacontaditera, 2 small prismated hexatera, 3 square-octahedral duoprisms, and 3 triangular-cuboctahedral duoprisms join at each vertex. As the name suggests, it is the biruncination of the hexeract.

Coordinates
The vertex coordinates of a small biprismated hexeract, centered at the origin and with unit edge length, are given by all permutations of:
 * $$\left(±\sqrt2,\,±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A birectified hexeract has the following Coxeter diagrams:
 * o4x3o3o3x3o (full symmetry)
 * x3o3x *b3o3x3o (D6 symmetry)