# Tetrachiliaenneacontahexahendon

(Redirected from 12-orthoplex)

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Tetrachiliaenneacontahexahendon | |
---|---|

Rank | 12 |

Type | Regular |

Space | Spherical |

Notation | |

Coxeter diagram | o4o3o3o3o3o3o3o3o3o3o3x |

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

Elements | |

Henda | 4096 dodecadaka |

Daka | 24576 hendecaxenna |

Xenna | 67584 decayotta |

Yotta | 112640 enneazetta |

Zetta | 126720 octaexa |

Exa | 101376 heptapeta |

Peta | 59136 hexatera |

Tera | 25344 pentachora |

Cells | 7920 tetrahedra |

Faces | 1769 triangles |

Edges | 264 |

Vertices | 24 |

Vertex figure | Dischiliatetracontoctadakon, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dihedral angle | |

Height | |

Central density | 1 |

Number of pieces | 4096 |

Level of complexity | 1 |

Related polytopes | |

Army | * |

Regiment | * |

Dual | Dodekeract |

Conjugate | None |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{12}, order 1961990553600 |

Convex | Yes |

Nature | Tame |

The **tetrachiliaenneacontahexahendon**, also called the **dodecacross** or **12-orthoplex**, is one of the 3 regular polyhenda. It has 4096 regular dodecadaka as facets, joining 4 to a xennon and 2048 to a vertex in a dischiliatetracontoctadakal arrangement. It is the 12-dimensional orthoplex. As such, it is a hexacontatetrapeton duotegum, hexadecachoron triotegum, octahedron tetrategum, and square hexategum.

## Vertex coordinates[edit | edit source]

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