Birectified hepteract

The birectified hepteract, or bersa, also called the birectified 7-cube, is a convex uniform polyexon. It consists of 14 birectified hexeracts and 128 rectified heptapeta. 4 rectified heptapeta and 5 birectified hexeracts join at each square-pentachoric duoprismatic vertex. As the name suggests, it is the birectification of the hepteract. It is also the rectified demihepteract.

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


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

Representations
A birectified hepteract has the following Coxeter diagrams:


 * o4o3x3o3o3o3o (full symmetry)
 * o3x3o *b3o3o3o3o (D7 symmetry, rectified demihepteract)
 * ooo4oxo3xox3ooo3ooo3ooo&#xt (B6 axial, birectified hexeract-first)