Octeract

Octeract
(OFF file)
Rank	8
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Octo
Coxeter diagram	x4o3o3o3o3o3o3o ()
Schläfli symbol	{4,3,3,3,3,3,3}
Tapertopic notation	11111111
Toratopic notation	IIIIIIII
Bracket notation	[IIIIIIII]
Elements
Zetta	16 hepteracts
Exa	112 hexeracts
Peta	448 penteracts
Tera	1120 tesseracts
Cells	1792 cubes
Faces	1792 squares
Edges	1024
Vertices	256
Vertex figure	Octaexon, edge length √2
Measures (edge length 1)
Circumradius	$\sqrt2 \approx 1.41421$
Inradius	$\frac12 = 0.5$
Hypervolume	1
Dizettal angle	90º
Height	1
Central density	1
Number of pieces	16
Level of complexity	1
Related polytopes
Army	Octo
Regiment	Octo
Dual	Diacosipentacontahexazetton
Conjugate	None
Abstract properties
Net count	2642657228
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B8, order 10321920
Convex	Yes
Nature	Tame

The octeract, or octo, also called the 8-cube, or hexadecazetton, is one of the 3 regular polyzetta. It has 16 hepteracts as facets, joining 8 to a vertex.

It is the 8-dimensional hypercube. It is a tesseractic duoprism and square tetraprism.

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

Vertex coordinates

The vertices of an octeract of edge length 1, centered at the origin, are given by:

• $\left(\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12,\,\pm\frac12\right).$

Representations

An octeract has the following Coxeter diarams:

• x4o3o3o3o3o3o3o (full symmetry)
• x x4o3o3o3o3o3o (hepteractic prism)
• xx4oo3oo3oo3oo3oo3oo&#x (B7 axial, hepteract atop hepteract)
• x4o3o3o x4o3o3o (tesseractic duoprism)

External links

• Klitzing, Richard. "octo".

• Wikipedia Contributors. "8-cube".