Birectified heptapeton

The birectified heptapeton, or bril, also called the birectified 6-simplex, is a convex uniform polypeton. It consists of 7 rectified hexatera and 7 dodecatera. 3 rectified hexatera and 4 dodecatera join at each triangular-tetrahedral prismatic vertex. As the name suggests, it is the birectification of the heptapeton.

It is also a convex segmentopeton, as a rectified hexateron atop dodecateron.

Vertex coordinates
The vertices of a birectified heptapeton of edge length 1 can be given in seven dimensions as all permutations of:


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

Representations
A birectified heptapeton has the following Coxeter diagrams:


 * o3o3x3o3o3o (full symmetry)
 * oo3xo3ox3oo3oo&#x (A5 axial, rectified hexateron atop dodecateron)
 * oxo xoo3oxo3oox3ooo&#xt (A4×A1 axial, pentachoron-first)
 * oxoo3ooxo oxoo3ooxo3ooox&#xt (A3×A2 axial, vertex-first)

Related polytopes
The birectified heptapeton is the colonel of a regiment of 18 members.