Hexadecaexon

The hexadecaexon, or he, also called the trirectified octaexon or trirectified 7-simplex, is a convex noble uniform polyexon. It consists of 16 birectified heptapeta. 8 birectified heptapeta join at each tetrahedral duoprismatic vertex. As the name suggests, it is the trirectification of the octaexon, the medial stage of truncation between an octaexon and the dual octaexon.

It is also a convex segmentoexon, as birectified heptapeton atop inverted birectified heptapeton.

A hexadecaexon can be vertex-inscribed into the pentacontahexapentacosiheptacontahexaexon (also known as the 231 polytope).

Vertex coordinates
The vertices of a hexadecaexon of edge length 1 can be given in eight dimensions as all permutations of:


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

Representations
A hexadecaexon has the following Coxeter diagrams:


 * o3o3o3x3o3o3o (full symmetry)
 * oo3oo3xo3ox3oo3oo&#x (A6 axial, birectified heptapeton atop alternate birectified heptapeton)