Hepteractihecatonicosoctaexon

The hepteractihecatonicosoctaexon, or sez, also called the trirectified hepteract or trirectified 7-cube, is a convex uniform polyexon. It consists of 14 birectified hexacontatetrapeta and 128 birectified heptapeta. 4 birectified hexacontatetrapeta and 8 birectified heptapeta join at each tetrahedral-octahedral duoprismatic vertex. It is hte medial stage in the series of truncations betweena hepteract and its dual hecatonicosoctaexon.

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


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

Representations
A hepteractihecatonicosoctaexon has the following Coxeter diagrams:


 * o4o3o3x3o3o3o (full symmetry)
 * o3o3o *b3x3o3o3o (D7 symmetry)
 * ooo4ooo3oxo3xox3ooo3ooo&#xt (B6 axial, birectified hexacontatetrapeton-first)