Birectified hecatonicosoctaexon

The birectified hecatonicosoctaexon, or barz, also called the birectified 7-orthoplex, is a convex uniform polyexon. It consists of 14 rectified hexacontatetrapeta and 128 birectified heptapeta. 3 rectified hexacontatetrapeta and 16 birectified heptapeta join at each triangular-hexadecachoric duoprismatic vertex. As the name suggests, it is the birectification of the hecatonicosoctaexon.

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


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

Representations
A birectified hecatonicosoctaexon has the following Coxeter diagrams:


 * o4o3o3o3x3o3o (full symmetry)
 * o3o3o *b3o3x3o3o (D7 symmetry)
 * ooo4ooo3ooo3oxo3xox3ooo&#xt (B6 axial, rectified hexacontatetrapeton-first)