# Octachiliahecatonenneacontadidokon

(Redirected from 13-orthoplex)

Octachiliahecatonenneacontadidokon | |
---|---|

Rank | 13 |

Type | Regular |

Notation | |

Coxeter diagram | x3o3o3o3o3o3o3o3o3o3o3o4o () |

Schläfli symbol | {3,3,3,3,3,3,3,3,3,3,3,4} |

Elements | |

Doka | 8192 tridecahenda |

Henda | 53248 dodecadaka |

Daka | 159744 hendecaxenna |

Xenna | 292864 decayotta |

Yotta | 366080 enneazetta |

Zetta | 329472 octaexa |

Exa | 219648 heptapeta |

Peta | 109824 hexatera |

Tera | 41184 pentachora |

Cells | 11440 tetrahedra |

Faces | 2288 triangles |

Edges | 312 |

Vertices | 26 |

Vertex figure | Tetrachiliaenneacontahexahendon, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dihedral angle | |

Height | |

Central density | 1 |

Number of external pieces | 8192 |

Level of complexity | 1 |

Related polytopes | |

Army | * |

Regiment | * |

Dual | Tridekeract |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{13}, order 51011754393600 |

Convex | Yes |

Nature | Tame |

The **octachiliahecatonenneacontadidokon**, also called the **tridecacross** or **13-orthoplex**, is a regular polydokon. It has 8192 regular tridecahenda as facets, joining 4 to a peak and 4096 to a vertex in a tetrachiliaenneacontahexahendal arrangement. It is the 13-dimensional orthoplex.

## Vertex coordinates[edit | edit source]

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

- .