# Tridekeract

Jump to navigation
Jump to search

Tridekeract | |
---|---|

Rank | 13 |

Type | Regular |

Space | Spherical |

Notation | |

Coxeter diagram | x4o3o3o3o3o3o3o3o3o3o3o3o |

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

Elements | |

Doka | 26 dodekeracts |

Henda | 312 hendekeracts |

Daka | 2288 dekeracts |

Xenna | 11440 enneracts |

Yotta | 41184 octeracts |

Zetta | 109824 hepteracts |

Exa | 219648 hexeracts |

Peta | 329472 penteracts |

Tera | 366080 tesseracts |

Cells | 292864 cubes |

Faces | 159744 squares |

Edges | 53248 |

Vertices | 8192 |

Vertex figure | Tridecahendon, edge length √2 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | 1 |

Dixennal angle | 90° |

Central density | 1 |

Number of pieces | 26 |

Level of complexity | 1 |

Related polytopes | |

Army | * |

Regiment | * |

Dual | Octachiliahecatonenneacontadidokon |

Conjugate | None |

Abstract properties | |

Euler characteristic | 2 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{13}, order 51011754393600 |

Convex | Yes |

Nature | Tame |

The **tridekeract**, also called the **13-cube** or **icosihexadokon**, is one of the 3 regular polydoka. It has 26 dodekeracts as facets, joining 3 to a dakon and 13 to a vertex.

It is the 13-dimensional hypercube.

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

## Vertex coordinates[edit | edit source]

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