Pentadekeract

The pentadekeract, also called the 15-cube or triacontatedakon, is one of the 3 regular polytedaka. It has 30 tetradekeracts as facets, joining 3 to a dokon and 15 to a vertex.

It is the 15-dimensional hypercube. As such it is a penteract trioprism and cube pentaprism.

It can be alternated into a demipentadekeract, which is uniform.

Vertex coordinates
The vertices of a pentadekeract of edge length 1, centered at the origin, are given by:
 * $$\left(\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12\right).$$