Chiliaicositetraxennon

The chiliaicositetraxennon, or ka, also called the decacross or 10-orthoplex, is one of the 3 regular polyxenna. It has 1024 regular decayotta as facets, joining 4 to an octaexon peak and 512 to a vertex in a pentacosidodecayottal arrangement. It is the 10-dimensional orthoplex. It is also a triacontaditeron duotegum and square pentategum.

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