# Octeract

Octeract Rank8
TypeRegular
SpaceSpherical
Notation
Bowers style acronymOcto
Coxeter diagramx4o3o3o3o3o3o3o (               )
Schläfli symbol{4,3,3,3,3,3,3}
Tapertopic notation11111111
Toratopic notationIIIIIIII
Bracket notation[IIIIIIII]
Elements
Zetta16 hepteracts
Exa112 hexeracts
Peta448 penteracts
Tera1120 tesseracts
Cells1792 cubes
Faces1792 squares
Edges1024
Vertices256
Vertex figureOctaexon, edge length 2
Measures (edge length 1)
Circumradius$\sqrt2 \approx 1.41421$ Inradius$\frac12 = 0.5$ Hypervolume1
Dizettal angle90º
Height1
Central density1
Number of pieces16
Level of complexity1
Related polytopes
ArmyOcto
RegimentOcto
DualDiacosipentacontahexazetton
ConjugateNone
Abstract properties
Net count2642657228
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB8, order 10321920
ConvexYes
NatureTame

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)