# 8-orthoplex

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8-orthoplex | |
---|---|

Rank | 8 |

Type | Regular |

Notation | |

Bowers style acronym | Ek |

Coxeter diagram | o4o3o3o3o3o3o3x () |

Schläfli symbol | {3,3,3,3,3,3,4} |

Bracket notation | <IIIIIIII> |

Elements | |

Zetta | 256 7-simplices |

Exa | 1024 6-simplices |

Peta | 1792 5-simplices |

Tera | 1792 pentachora |

Cells | 1120 tetrahedra |

Faces | 448 triangles |

Edges | 112 |

Vertices | 16 |

Vertex figure | 7-orthoplex, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dizettal angle | |

Height | |

Central density | 1 |

Number of external pieces | 256 |

Level of complexity | 1 |

Related polytopes | |

Army | Ek |

Regiment | Ek |

Dual | 8-cube |

Conjugate | None |

Abstract & topological properties | |

Flag count | 10321920 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{8}, order 10321920 |

Convex | Yes |

Net count | 2642657228 |

Nature | Tame |

The **8-orthoplex**, also called the **octacross**, **diacosipentacontahexazetton**, or **ek**, is a regular 8-polytope. It has 256 regular 7-simplices as facets, joining 4 to a 5-simplex peak and 128 to a vertex in a 7-orthoplecial arrangement. It is the 8-dimensional orthoplex. It is also a hexadecachoric duotegum and square tetrategum.

## Vertex coordinates[edit | edit source]

The vertices of a regular 8-orthoplex of edge length 1, centered at the origin, are given by all permutations of:

- .

## Representations[edit | edit source]

A regular 8-orthoplex has the following Coxeter diagrams:

- o4o3o3o3o3o3o3x () (full symmetry)
- o3o3o3o3o3o3x *b3o () (D
_{8}symmetry) - xo3oo3oo3oo3oo3oo3ox&#x (A
_{7}axial, octaexic antiprism) - ooo4ooo3ooo3ooo3ooo3ooo3oxo&#xt (B
_{7}axial, hecatonicosoctaexal tegum)

## External links[edit | edit source]

- Klitzing, Richard. "ek".
- Wikipedia contributors. "8-orthoplex".