Dodekeract

The dodekeract, also called the 12-cube or icositetrahendon, is one of the 3 regular polyhenda. It has 24 hendekeracts as facets, joining 3 to a xennon and 12 to a vertex.

It is the 12-dimensional hypercube. As such, it is a hexeract duoprism, tesseract trioprism, cube tetraprism and square hexaprism.

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

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