Demihexeract

The demihexeract, or hax, also called the hemihexeract or 6-demicube, is a convex uniform polypeton. It has 12 demipenteracts and 32 hexatera as facets, with 6 of each at a vertex forming a rectified hexateron as the vertex figure. It is the 6-dimensional demihypercube and is formed by alternating the hexeract.

It is a segmentopeton, as a demipenteractic antiprism. It is also a tetrahedral duoantiprism and digonal trioantiprism.

The demihexeract contains the vertices of a tetrahedral duoprism.

Vertex coordinates
The vertices of a demihexeract of edge length 1, centered at the origin, are given by all even sign changes of:
 * ($\sqrt{3}$/4, $\sqrt{2}$/4, $\sqrt{6}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4).

Representations
A demihexeract has the folowing Coxeter diagrams:


 * x3o3o *b3o3o3o (full symmetry)
 * s4o3o3o3o3o (as alternated hexeract)
 * xo3oo3ox *b3oo3oo&#x (D5 axial, demipenteract antiprism)
 * xoo3ooo3oxo3ooo3oox&#xt (A5 axial, hexateron-first)
 * oooo3oxoo3oooo3ooxo3oooo&#x (A5 axial, vertex-first)
 * oxo xox3ooo3ooo *c3oxo&#xt (D4×A1 axial, hexadecachoron-first)
 * xo3oo3ox *b3oo xo ox&#zx (D4×A1×A1 symmetry)
 * oxoo3ooxo xoxo3oooo3oxox&#xt (A3×A2 axial, tetrahedron-first)
 * xo3oo3ox xo3oo3ox&#zx (A3×A3 symmetry, hull of two tetrahedral duoprisms)