Diacosipentacontahexazetton

The Diacosipentacontahexazetton, or ek, also called the octacross or 8-orthoplex, is one of the 3 regular polyzetta. It has 128 regular octaexa as facets, joining 4 to a hexateron peak and 64 to a vertex in a hecatonicosoctaexal arrangement. It is the 8-dimensional orthoplex. It is also a hexadecachoron 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:
 * (±$\sqrt{2}$/2, 0, 0, 0, 0, 0, 0, 0).