# Hendekeract

(Redirected from 11-hypercube)

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Hendekeract | |
---|---|

Rank | 11 |

Type | Regular |

Space | Spherical |

Info | |

Coxeter diagram | x4o3o3o3o3o3o3o3o3o3o |

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

Symmetry | B11, order 81749606400 |

Army | * |

Regiment | * |

Elements | |

Vertex figure | Hendecaxennon, edge length √2 |

Daka | 22 dekeracts |

Xenna | 220 enneracts |

Yotta | 1320 octeracts |

Zetta | 5280 hepteracts |

Exa | 14784 hexeracts |

Peta | 29568 penteracts |

Tera | 42240 tesseracts |

Cells | 42240 cubes |

Faces | 28160 squares |

Edges | 11264 |

Vertices | 2048 |

Measures (edge length 1) | |

Circumradius | √11/2 ≈ 1.65831 |

Inradius | 1/2 = 0.5 |

Hypervolume | 1 |

Dixennal angle | 90° |

Central density | 1 |

Euler characteristic | 2 |

Related polytopes | |

Dual | Dischiliatetracontoctadakon |

Conjugate | Hendekeract |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **hendekeract**, also called the **11-cube** or **icosididakon**, is one of the 3 regular polydaka. It has 22 dekeracts as facets, joining 3 to a yotton and 11 to a vertex.

It is the 11-dimensional hypercube.

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

A regular dodecadakon of edge length √6 can be inscribed in the hendekeract. The next largest simplex that can be inscribed in a hypercube is the hexadecatedakon.^{[1]}

## Vertex coordinates[edit | edit source]

The vertices of a hendekeract 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).

## References[edit | edit source]

- ↑ Sloane, N. J. A. (ed.). "Sequence A019442".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.