Demihepteract

The demihepteract, or hesa, also called the hemihepteract or 7-demicube, is a convex uniform polyexon. It has 14 demihexeracts and 64 heptapeta as facets, with 7 of each at a vertex forming a rectified heptapeton as the vertex figure. It is the 7-dimensional demihypercube and is formed by alternating the hepteract. It is also a segmentopeton, as a demihexeractic antiprism.

The demihepteract contains the vertices of a tetrahedral-hexadecachoric duoprism.

Vertex coordinates
The vertices of a demihepteract of edge length 1, centered at the origin, are given by all even sign changes of:
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
A demihepteract has the folowing Coxeter diagrams:


 * x3o3o *b3o3o3o3o (full symmetry)
 * s4o3o3o3o3o3o (as alternated hepteract)
 * xo3oo3ox *b3oo3oo3oo&#x (D6 axial, demihexeract antiprism)
 * oooo3oxoo3oooo3ooxo3oooo3ooox&#xt (A6 axial, vertex-first)
 * oxoo3ooxo xoxo3oooo3oxox *d3oooo&#xt (D4×A2 symmetry, hexadecachoron-first)
 * xo3oo3ox *b3oo xo3oo3ox&#zx (D4×A3 symmetry, hull of two tetrahedral-hexadecachoric duoprisms)