# Hexadekeract

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Hexadekeract | |
---|---|

Rank | 16 |

Type | Regular |

Space | Spherical |

Notation | |

Coxeter diagram | x4o3o3o3o3o3o3o3o3o3o3o3o3o3o3o |

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

Elements | |

Pedaka | 32 pentadekeracts |

Tedaka | 480 tetradekeracts |

Tradaka | 4480 tridekeracts |

Doka | 29120 dodekeracts |

Henda | 139776 hendekeracts |

Daka | 512512 dekeracts |

Xenna | 1464320 enneracts |

Yotta | 3294720 octeracts |

Zetta | 5857280 hepteracts |

Exa | 8200192 hexeracts |

Peta | 8945664 penteracts |

Tera | 7454720 tesseracts |

Cells | 4587520 cubes |

Faces | 1966080 squares |

Edges | 524288 |

Vertices | 65536 |

Vertex figure | Hexadecatedakon, edge length √2 |

Measures (edge length 1) | |

Circumradius | 2 |

Inradius | |

Hypervolume | 1 |

Dixennal angle | 90° |

Height | 1 |

Central density | 1 |

Number of pieces | 32 |

Level of complexity | 1 |

Related polytopes | |

Army | * |

Regiment | * |

Dual | Hexamyriapentachiliapentacositriacontahexapedakon |

Conjugate | None |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{16}, order 1371195958099968000 |

Convex | Yes |

Nature | Tame |

The **hexadekeract**, also called the **16-cube** or **triacontadipedakon**, is one of the 3 regular polypedaka. It has 32 pentadekeracts as facets, joining 3 to a tradakon and 16 to a vertex.

It is the 16-dimensional hypercube. As such it is an octeract duoprism, tesseract tetraprism, and square octaprism.

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

## Vertex coordinates[edit | edit source]

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