Rectified hexeract

The rectified hexeract or rax, also called the rectified 6-cube, is a convex uniform polypeton. It consists of 64 regular hexatera and 12 rectified penteracts. Two hexatera and 5 rectified penteracts join at each pentachoric prismatic vertex. As the name suggests, it is the rectification of the hexeract.

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


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

Representations
A rectified hexeract has the following Coxeter diagrams:


 * o4x3o3o3o3o (full symmetry)
 * x3o3x *b3o3o3o (D6 symmetry)
 * oqo4xox3ooo3ooo3ooo&#xt (B5 axial, rectified penteract-first)
 * xxoooo3oxxooo3ooxxoo3oooxxo3ooooxx&#xt (A5 axial, hexateron-first)