Birectified hexeract

The birectified hexeract, or brox, also called the birectified 6-cube, is a convex uniform polypeton. It consists of 12 penteractitriacontaditera and 64 rectified hexatera. 4 rectified hexatera and 4 penteractitriacontaditera join at each square-tetrahedral duoprismatic vertex. As the name suggests, it is the birectification of the hexeract. It is also the rectified demihexeract.

The birectified hexeract contains the vertices of a square-rectified tesseractic duoprism and cuboctahedral duoprism.

Vertex coordinates
The vertices of a birectified hexeract of edge length 1 are given by all permutations of:


 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right).$$

Representations
A birectified hexeract has the following Coxeter diagrams:


 * o4o3o3o3x3o (full symmetry)
 * o3x3o *b3o3o3o (D6 symmetry, rectified demihexeract)
 * ooo4oxo3xox3ooo3ooo&#xt (BC5 axial, penteractitriacontaditeron-first)
 * oxo3xox3oxo *b3ooo3ooo&#xt (D5 symmetry, same as above with half symmetry)
 * oxooo3xoxoo3oxoxo3ooxox3oooxo&#xt (A5 axial, rectified hexateron-first)