Demiocteract

Demiocteract
(OFF file)
Rank	8
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Hocto
Coxeter diagram	x3o3o *b3o3o3o3o3o ()
Elements
Zetta	128 octaexa, 16 demihepteracts
Exa	1024 heptapeta, 112 demihexeracts
Peta	3584 hexatera, 448 demipenteracts
Tera	7168 pentachora, 1120 hexadecachora
Cells	1792+8960 tetrahedra
Faces	7168 triangles
Edges	1792
Vertices	128
Vertex figure	Rectified octaexon, edge length 1
Measures (edge length 1)
Circumradius	1
Hypervolume	$\frac{157}{2520} ≈ 0.062302$
Dizettal angles	Hesa–hop–oca: $\arccos\left(-\frac{\sqrt2}{4}\right) ≈ 110.70481°$
	Hesa–hax–hesa: 90°
Height	$\frac{\sqrt2}{2} ≈ 0.70711$
Central density	1
Number of pieces	144
Level of complexity	6
Related polytopes
Army	Hocto
Regiment	Hocto
Dual	Semistellated diacosipentacontahexazetton‎
Conjugate	None
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	D8, order 5160960
Convex	Yes
Nature	Tame

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 segmentozetton, 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)

External links

• Klitzing, Richard. "hocto".

• Wikipedia Contributors. "8-demicube".