8-cube

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8-cube
Rank8
TypeRegular
Notation
Bowers style acronymOcto
Coxeter diagramx4o3o3o3o3o3o3o ()
Schläfli symbol{4,3,3,3,3,3,3}
Tapertopic notation11111111
Toratopic notationIIIIIIII
Bracket notation[IIIIIIII]
Elements
Zetta16 7-cubes
Exa112 6-cubes
Peta448 5-cubes
Tera1120 tesseracts
Cells1792 cubes
Faces1792 squares
Edges1024
Vertices256
Vertex figure7-simplex, edge length 2
Measures (edge length 1)
Circumradius
Inradius
Hypervolume1
Dizettal angle90°
Height1
Central density1
Number of external pieces16
Level of complexity1
Related polytopes
ArmyOcto
RegimentOcto
Dual8-orthoplex
ConjugateNone
Abstract & topological properties
Flag count10321920
Euler characteristic0
OrientableYes
Properties
SymmetryB8, order 10321920
ConvexYes
Net count2642657228[1]
NatureTame

The 8-cube, also called the octeract, or octo, or hexadecazetton, is one of the 3 regular 8-polytopes. It has 16 7-cubes 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 8-demicube, which is uniform.

Vertex coordinates[edit | edit source]

The vertices of an 8-cube of edge length 1, centered at the origin, are given by:

  • .

Representations[edit | edit source]

An 8-cube has the following Coxeter diagrams:

  • x4o3o3o3o3o3o3o () (full symmetry)
  • x x4o3o3o3o3o3o () (hepteractic prism)
  • xx4oo3oo3oo3oo3oo3oo&#x (B7 axial, hepteract atop hepteract)
  • x4o3o3o x4o3o3o () (tesseractic duoprism)
  • x4o x4o x4o x4o () (square tetraprism)

External links[edit | edit source]

References[edit | edit source]

  1. "A091159". The On-line Encyclopedia of Integer Sequences. Retrieved 2022-12-07.