# Pentadekeract

(Redirected from 15-hypercube)

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Pentadekeract | |
---|---|

Rank | 15 |

Type | Regular |

Space | Spherical |

Info | |

Coxeter diagram | x4o3o3o3o3o3o3o3o3o3o3o3o3o3o |

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

Symmetry | B15, order 42849873690624000 |

Army | * |

Regiment | * |

Elements | |

Vertex figure | Pentadecatradakon, edge length √2 |

Tedaka | 30 tetradekeracts |

Tradaka | 420 tridekeracts |

Doka | 3640 dodekeracts |

Henda | 21840 hendekeracts |

Daka | 96096 dekeracts |

Xenna | 320320 enneracts |

Yotta | 823680 octeracts |

Zetta | 1647360 hepteracts |

Exa | 2562560 hexeracts |

Peta | 3075072 penteracts |

Tera | 2795520 tesseracts |

Cells | 1863680 cubes |

Faces | 860160 squares |

Edges | 245760 |

Vertices | 32768 |

Measures (edge length 1) | |

Circumradius | √15/2 ≈ 1.93649 |

Inradius | 1/2 = 0.5 |

Hypervolume | 1 |

Dixennal angle | 90° |

Central density | 1 |

Euler characteristic | 2 |

Related polytopes | |

Dual | Trismyriadischiliaheptacosihexacontoctatedakon |

Conjugate | Pentadekeract |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **pentadekeract**, also called the **15-cube** or **triacontatedakon**, is one of the 3 regular polytedaka. It has 30 tetradekeracts as facets, joining 3 to a dokon and 15 to a vertex.

It is the 15-dimensional hypercube. As such it is a penteract trioprism and cube pentaprism.

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

## Vertex coordinates[edit | edit source]

The vertices of a pentadekeract 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, ±1/2, ±1/2, ±1/2).