# Octeract

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Octeract | |
---|---|

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 | |

Inradius | |

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^{[1]} |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{8}, 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[edit | edit source]

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

## Representations[edit | edit source]

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[edit | edit source]

- Klitzing, Richard. "octo".

- Wikipedia Contributors. "8-cube".