Diacosipentacontahexazetton

The Diacosipentacontahexazetton, or ek, also called the octacross or 8-orthoplex, is one of the 3 regular polyzetta. It has 256 regular octaexa as facets, joining 4 to a hexateron peak and 128 to a vertex in a hecatonicosoctaexal arrangement. It is the 8-dimensional orthoplex. It is also a hexadecachoric duotegum and square tetrategum.

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