Hecatonicosoctaexon

The hecatonicosoctaexon, or zee, also called the heptacross or 7-orthoplex, is one of the 3 regular polyexa. It has 128 regular heptapeta as facets, joining 4 to a pentachoron peak and 64 to a vertex in a hexacontatetrapetal arrangement. It is the 7-dimensional orthoplex.

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).