Trismyriadischiliaheptacosihexacontoctatedakon

The trismyriadischiliaheptacosihexacontaoctatedakon, also called the pentadecacross or 15-orthoplex, is one of the 3 regular polytedaka. It has 32768 regular pentadecatradaka as facets, joining 4 to a dokon and 16384 to a vertex in a myriahexachiliatriacosioctacontatetratradakal arrangement. It is the 15-dimensional orthoplex. As such it is a triacontaditeron triotegum and octahedron pentategum.

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