Great birhombated hexeract

The great birhombated hexeract or gaborx, also called the bicantitruncated dodecapeton or bicantitruncated 6-cube, is a convex uniform polypeton. It consists of 12 great birhombated penteracts, 64 great rhombated hexatera, and 240 square-tetrahedral duoprisms. 3 great birhombated penteracts, 2 great rhombated hexatera, and 1 square-tetrahedral duoprism join at each vertex. As the name suggests, it is the bicantitruncation of the hexeract.

Coordinates
The vertex coordinates of a great birhombated hexeract, centered at the origin and with unit edge length, are given by all permutations of:
 * $$\left(±\frac{3\sqrt2}{2},\,±\frac{3\sqrt2}{2},\,±\frac{3\sqrt2}{2},\,±\sqrt2,\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A birectified hexeract has the following Coxeter diagrams:
 * o4x3x3x3o3o (full symmetry)
 * x3x3x *b3x3o3o (D6 symmetry)