# Dodekeract

(Redirected from 12-hypercube)

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Dodekeract | |
---|---|

Rank | 12 |

Type | Regular |

Space | Spherical |

Info | |

Coxeter diagram | x4o3o3o3o3o3o3o3o3o3o3o |

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

Symmetry | B12, order 1961990553600 |

Army | * |

Regiment | * |

Elements | |

Vertex figure | Dodecadakon, edge length √2 |

Henda | 24 hendekeracts |

Daka | 264 dekeracts |

Xenna | 1760 enneracts |

Yotta | 7920 octeracts |

Zetta | 25344 hepteracts |

Exa | 59136 hexeracts |

Peta | 101376 penteracts |

Tera | 126720 tesseracts |

Cells | 112640 cubes |

Faces | 67584 squares |

Edges | 24576 |

Vertices | 4096 |

Measures (edge length 1) | |

Circumradius | √3 ≈ 1.73205 |

Inradius | 1/2 = 0.5 |

Hypervolume | 1 |

Dixennal angle | 90° |

Central density | 1 |

Euler characteristic | 0 |

Related polytopes | |

Dual | Tetrachiliaenneacontahexahendon |

Conjugate | Dodekeract |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **dodekeract**, also called the **12-cube** or **icositetrahendon**, is one of the 3 regular polyhenda. It has 24 hendekeracts as facets, joining 3 to a xennon and 12 to a vertex.

It is the 12-dimensional hypercube. As such, it is a hexeract duoprism, tesseract trioprism, cube tetraprism and square hexaprism.

It can be alternated into a demidodekeract, which is uniform.

## Vertex coordinates[edit | edit source]

The vertices of a dodekeract of edge length 1, centered at the origin, are given by:

- (±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2).