Stellated hexadecaexon

The stellated hexadecaexon or she is the simplest regular compound polyexon, and the sixth in an infinite series of regular bi-simplex compounds. It is a compound of two octaexa in dual orientations. It has 16 heptapeta as exa, with 7 exa joining at a vertex. As the name suggests, it is also a stellation of the uniform hexadecaexon.

The vertices of a regular octaexon of edge length 1, centered at the origin, are given by:

Vertex coordinates

 * $$±\left(±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30},\,-\frac{\sqrt{21}}{42},\,-\frac{\sqrt7}{28}\right),$$
 * $$±\left(0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30},\,-\frac{\sqrt{21}}{42},\,-\frac{\sqrt7}{28}\right),$$
 * $$±\left(0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30},\,-\frac{\sqrt{21}}{42},\,-\frac{\sqrt7}{28}\right),$$
 * $$±\left(0,\,0,\,0,\,\frac{\sqrt{10}}{5},\,-\frac{\sqrt{15}}{30},\,-\frac{\sqrt{21}}{42},\,-\frac{\sqrt7}{28}\right),$$
 * $$±\left(0,\,0,\,0,\,0,\,\frac{\sqrt{15}}{6},\,-\frac{\sqrt{21}}{42},\,-\frac{\sqrt7}{28}\right),$$
 * $$±\left(0,\,0,\,0,\,0,\,0,\,\frac{\sqrt{21}}{7},\,-\frac{\sqrt7}{28}\right),$$
 * $$\left(0,\,0,\,0,\,0,\,0,\,0,\,±\frac{\sqrt7}{4}\right).$$