Tetrachiliaenneacontahexahendon

The tetrachiliaenneacontahexahendon, also called the dodecacross or 12-orthoplex, is one of the 3 regular polyhenda. It has 4096 regular dodecadaka as facets, joining 4 to a xennon and 2048 to a vertex in a dischiliatetracontoctadakal arrangement. It is the 12-dimensional orthoplex. As such, it is a hexacontatetrapeton duotegum, hexadecachoron triotegum, octahedron tetrategum, and square hexategum.

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