Rectified octeract

The rectified octeract, or recto, also called the rectified 8-cube, is a convex uniform polyzetton. It consists of 16 rectified hepteracts and 256 regular octaexa. Two octaexa and 7 rectified hepteracts join at each heptapetic prismatic vertex. As the name suggests, it is the rectification of the octeract.

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


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

Representations
A rectified octeract has the following Coxeter diagrams:


 * o4x3o3o3o3o3o3o (full symmetry)
 * x3o3x *b3o3o3o3o3o (D8 symmetry)