Truncated hexeract

The truncated hexeract or tox, also called the truncated 6-cube, is a convex uniform polypeton. It consists of 12 truncated penteracts and 64 hexatera. 5 truncated penteracts and 1 hexateron join at each vertex. As the name suggests, it is the truncation of the hexeract.

Vertex coordinates
The vertices of a truncated hexeract of edge length 1 are given by all permutations of:
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$