# Hendecagonal-cubic duoprism

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Hendecagonal-cubic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hencube |

Coxeter diagram | x11o x4o3o |

Elements | |

Tera | 11 tesseracts, 6 square-hendecagonal duoprisms |

Cells | 11+66 cubes, 12 hendecagonal prisms |

Faces | 66+132 squares, 8 hendecagons |

Edges | 88+132 |

Vertices | 88 |

Vertex figure | Triangular scalene, edge lengths 2cos(π/11) (top), √2 (base triangle and sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tes–cube–tes: |

Tes–cube–shendip: 90° | |

Shendip–henp–shendip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 17 |

Level of complexity | 10 |

Related polytopes | |

Army | Hencube |

Regiment | Hencube |

Dual | Hendecagonal-octahedral duotegum |

Conjugates | Small hendecagrammic-cubic duoprism, Hendecagrammic-cubic duoprism, Great hendecagrammic-cubic duoprism, Grand hendecagrammic-cubic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(11), order 1056 |

Convex | Yes |

Nature | Tame |

The **hendecagonal-cubic duoprism** or **hencube**, also known as the **square-hendecagonal duoprismatic prism**, is a convex uniform duoprism that consists of 11 tesseracts and 6 square-hendecagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-hendecagonal duoprisms. It is a duoprism based on a square and a hendecagonal prism, which makes it a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a hendecagonal-cubic duoprism of edge length 2sin(π/11) are given by:

where j = 2, 4, 6, 8, 10.

## Representations[edit | edit source]

A hendecagonal-cubic duoprism has the following Coxeter diagrams:

- x11o x4o3o (full symmetry)
- x x4o x11o (square-hendecagonal duoprismatic prism)
- x x x x11o (hendecagonal prismatic prismatic prism)