Birectified octeract

The birectified octeract, or bro, also called the birectified 8-cube, is a convex uniform polyzetton. It consists of 16 birectified hepteracts and 256 rectified octaexa. 4 rectified octaexa and 6 birectified hepteracts join at each square-hexateric duoprismatic vertex. As the name suggests, it is the birectification of the octeract. It is also the rectified demiocteract.

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


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

Representations
A birectified octeract has the following Coxeter diagrams:


 * o4o3x3o3o3o3o3o (full symmetry)
 * o3x3o *b3o3o3o3o3o (D8 symmetry, rectified demiocteract)
 * ooo4oxo3xox3ooo3ooo3ooo3ooo&#xt (B7 axial, birectified hepteract-first)