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:
 * $$\left(\pm\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0,\,0,\,0\right).$$

Representations
A regular diacosipentacontahexazetton has the following Coxeter diagrams:


 * o4o3o3o3o3o3o3x (full symmetry)
 * o3o3o *b3o3o3o3o3x (D8 symmetry)
 * xo3oo3oo3oo3oo3oo3ox&#x (A7 axial, octaexic antiprism)
 * ooo4ooo3ooo3ooo3ooo3ooo3oxo&#xt (B7 axial, hecatonicosoctaexal tegum)