# 9-orthoplex

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9-orthoplex | |
---|---|

Rank | 9 |

Type | Regular |

Notation | |

Bowers style acronym | Vee |

Coxeter diagram | o4o3o3o3o3o3o3o3x () |

Schläfli symbol | {3,3,3,3,3,3,3,4} |

Bracket notation | <IIIIIIIII> |

Elements | |

Yotta | 512 enneazetta |

Zetta | 2304 octaexa |

Exa | 4608 heptapeta |

Peta | 5376 hexatera |

Tera | 4032 pentachora |

Cells | 2016 tetrahedra |

Faces | 672 triangles |

Edges | 144 |

Vertices | 18 |

Vertex figure | 8-orthoplex, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Diyottal angle | |

Height | |

Central density | 1 |

Number of external pieces | 512 |

Level of complexity | 1 |

Related polytopes | |

Army | Vee |

Regiment | Vee |

Dual | 9-cube |

Conjugate | None |

Abstract & topological properties | |

Flag count | 185794560 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{9}, order 185794560 |

Flag orbits | 1 |

Convex | Yes |

Net count | 248639631948 |

Nature | Tame |

The **9-orthoplex**, also called the **enneacross**, **pentacosidodecayotton**, or **vee**, is one of the 3 regular 9-polytopes. It has 512 regular 8-simplices as facets, joining 4 to a 6-simplex peak and 256 to a vertex in a 8-orthoplecial arrangement. It is the 9-dimensional orthoplex. It is also an octahedron triotegum.

## Vertex coordinates[edit | edit source]

The vertices of a regular 9-orthoplex of edge length 1, centered at the origin, are given by all permutations of:

- .

## External links[edit | edit source]

- Klitzing, Richard. "vee".
- Wikipedia contributors. "9-orthoplex".