Pentacosidodecayotton

The pentacosidodecayotton, or vee, also called the enneacross or 9-orthoplex, is one of the 3 regular polyyotta. It has 512 regular enneazetta as facets, joining 4 to a heptapeton peak and 256 to a vertex in a diacosipentacontahexazettal arrangement. It is the 9-dimensional orthoplex. It is also an octahedron triotegum.

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