Hepteract

The hepteract, or hept, also called the 7-cube, or tetradecaexon, is one of the 3 regular polyexa. It has 14 hexeracts as facets, joining 7 to a vertex. It is the 7-dimensional hypercube.

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

A regular octaexon of edge length 2 can be inscribed in the unit hepteract. The next largest simplex that can be inscribed in a hypercube is the dodecadakon.

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

Representations
A hepteract has the following Coxeter diagrams:


 * x4o3o3o3o3o3o (full symmetry)
 * x x4o3o3o3o3o (BC6×A1 symmetry, hexxeractic prism)
 * x4o x4o3o3o3o (BC5×BC2 symmetry, square-penteractic duoprism)
 * x4o3o x4o3o3o (BC4×BC3 symmetry, cubic-tesseractic duoprism)
 * xx4oo3oo3oo3oo3oo&#x (BC6 axial)
 * oqoooooo3ooqooooo3oooqoooo3ooooqooo3oooooqoo3ooooooqo&#xt (A6 axial, vertex-first)