Hexadekeract

The hexadekeract, also called the 16-cube or triacontadipedakon, is one of the 3 regular polypedaka. It has 32 pentadekeracts as facets, joining 3 to a tradakon and 16 to a vertex.

It is the 16-dimensional hypercube. As such it is an octeract duoprism, tesseract tetraprism, and square octaprism.

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

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