Demiocteract

The demiocteract, or hocto, also called the hemiocteract or 8-demicube, is a convex uniform polyzetton. It has 16 demihepteracts and 128 octaexa as facets, with 8 of each at a vertex forming a rectified octaexon as the vertex figure. It is the 8-dimensional demihypercube and is formed by alternating the octeract. It is also a segmentopeton, as a demihepteractic antiprism.

The demiocteract can also be seen as the convex hull of two opposite hexadecachoric duoprisms, and also contains the vertices of a tetrahedral-demipenteractic duoprism. A unit demiocteract can be vertex-inscribed into the Dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton (the E8 polytope or 421 polytope).

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

Representations
A demiocteract has the folowing Coxeter diagrams:


 * x3o3o *b3o3o3o3o3o (full symmetry)
 * s4o3o3o3o3o3o3o (as alternated octeract)
 * xo3oo3ox *b3oo3oo3oo3oo&#x (D7 axial, demihepteract antiprism)
 * xooo3oooo3oxoo3oooo3ooxo3oooo3ooox&#xt (A7 axial, octaexon-first)
 * ooooo3oxooo3ooooo3ooxoo3ooooo3oooxo3ooooo&#xt (A7 axial, vertex-first)
 * xo3oo3ox *b3oo xo3oo3ox *f3oo&#zx (hull of two hexadeecachoric duoprisms)