Hexamyriapentachiliapentacositriacontahexapedakon

The hexamyriapentachiliapentacositriacontahexapedakon, also called the hexadecacross or 16-orthoplex, is one of the 3 regular polypedaka. It has 65536 regular hexadecatedaka as facets, joining 4 to a tradakon and 32768 to a vertex in a trismyriadischiliaheptacosihexacontoctatedakal arrangement. It is the 16-dimensional orthoplex. As such it is a diacosipentacontahexazetton duotegum, hexadecachoron tetrategum, and square octategum.

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