Birectified enneazetton

The birectified enneazetton, or brene, also called the birectified 8-simplex, is a convex uniform polyzetton. It consists of 9 rectified octaexa and 9 birectified octaexa. 3 rectified octaexa and 6 birectified octaexa join at each triangular-hexateric duoprismatic vertex. As the name suggests, it is the birectification of the enneazetton.

It is also a convex segmentozetton, as rectified octaexon atop birectified octaexon.

A unit birectified enneazetton can be vetex inscibed into the dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton (also konwn as the 421 polytope).

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


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

Representations
A birectified enneazetton has the following Coxeter diagrams:


 * o3o3x3o3o3o3o3o (full symmetry)
 * oo3xo3ox3oo3oo3oo3oo&#x (A7 axial, rectified octaexon atop birectified octaexon)