Rectified hecatonicosoctaexon

The rectified hecatonicosoctaexon, or rez, also called the rectified 7-orthoplex, is a convex uniform polyexon. It consists of 14 regular hexacontatetrapeta and 128 rectified heptapeta. Two hexacontatetrapeta and 32 rectified heptapeta join at each triacontaditeric prismatic vertex. As the name suggests, it is the rectification of the hecatonicosoctaexon.

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


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

Representations
A rectified hecatonicosoctaexon has the following Coxeter diagrams:


 * o4o3o3o3o3x3o (full symmetry)
 * o3o3o *b3o3o3x3o (D7 symmetry)
 * ooo4ooo3ooo3ooo3oxo3xox&#xt (B6 axial, hexacontatetrapeton-first)