Octeract

The octeract, or octo, also called the 8-cube, or hexadecazetton, is one of the 3 regular polyzetta. It has 16 hepteracts as facets, joining 8 to a vertex.

It is the 8-dimensional hypercube. It is a tesseractic duoprism and square tetraprism.

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

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

Representations
An octeract has the following Coxeter diarams:


 * x4o3o3o3o3o3o3o (full symmetry)
 * x x4o3o3o3o3o3o (hepteractic prism)
 * xx4oo3oo3oo3oo3oo3oo&#x (B7 axial, hepteract atop hepteract)
 * x4o3o3o x4o3o3o (tesseractic duoprism)