Octachiliahecatonenneacontadidokon

The octachiliahecatonenneacontadidokon, also called the tridecacross or 13-orthoplex, is one of the 3 regular polydoka. It has 8192 regular tridecahenda as facets, joining 4 to a dakon and 4096 to a vertex in a tetrachiliaenneacontahexahendal arrangement. It is the 13-dimensional orthoplex.

Vertex coordinates
The vertices of a regular octachiliahecatonenneacontadidokon of edge length 1, centered at the origin, are given by all permutations of:
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0\right).$$