# Hendecagonal duoprism

(Redirected from 11-11 duoprism)

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Handip |

Info | |

Coxeter diagram | x11o x11o |

Symmetry | I2(11)≀S2, order 968 |

Army | Handip |

Regiment | Handip |

Elements | |

Vertex figure | Tetragonal disphenoid, edge lengths 2cos(π/11) (bases) and √2 (sides) |

Cells | 22 hendecagonal prisms |

Faces | 121 squares, 22 hendecagons |

Edges | 242 |

Vertices | 121 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Henp–11–henp: |

Henp–4–henp: 90° | |

Central density | 1 |

Euler characteristic | 0 |

Number of pieces | 22 |

Level of complexity | 3 |

Related polytopes | |

Dual | Hendecagonal duotegum |

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

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **hendecagonal duoprism** or **handip**, also known as the **hendecagonal-hendecagonal duoprism**, the **11 duoprism** or the **11-11 duoprism**, is a noble uniform duoprism that consists of 22 hendecagonal prisms, with 4 joining at each vertex. It is also the 22-10 gyrochoron. It is the first in an infinite family of isogonal hendecagonal dihedral swirlchora and also the first in an infinite family of isochoric hendecagonal hosohedral swirlchora.

## Vertex coordinates[edit | edit source]

The coordinates of a hendecagonal duoprism, centered at the origin and with edge length 2sin(π/11), are given by:

- (1, 0, 1, 0),
- (1, 0, cos(2π/11), ±sin(2π/11)),
- (1, 0, cos(4π/11), ±sin(4π/11)),
- (1, 0, cos(6π/11), ±sin(6π/11)),
- (1, 0, cos(8π/11), ±sin(8π/11)),
- (1, 0, cos(10π/11), ±sin(10π/11)),
- (cos(2π/11), ±sin(2π/11), 1, 0),
- (cos(2π/11), ±sin(2π/11), cos(2π/11), ±sin(2π/11)),
- (cos(2π/11), ±sin(2π/11), cos(4π/11), ±sin(4π/11)),
- (cos(2π/11), ±sin(2π/11), cos(6π/11), ±sin(6π/11)),
- (cos(2π/11), ±sin(2π/11), cos(8π/11), ±sin(8π/11)),
- (cos(2π/11), ±sin(2π/11), cos(10π/11), ±sin(10π/11)),
- (cos(4π/11), ±sin(4π/11), 1, 0),
- (cos(4π/11), ±sin(4π/11), cos(2π/11), ±sin(2π/11)),
- (cos(4π/11), ±sin(4π/11), cos(4π/11), ±sin(4π/11)),
- (cos(4π/11), ±sin(4π/11), cos(6π/11), ±sin(6π/11)),
- (cos(4π/11), ±sin(4π/11), cos(8π/11), ±sin(8π/11)),
- (cos(4π/11), ±sin(4π/11), cos(10π/11), ±sin(10π/11)),
- (cos(6π/11), ±sin(6π/11), 1, 0),
- (cos(6π/11), ±sin(6π/11), cos(2π/11), ±sin(2π/11)),
- (cos(6π/11), ±sin(6π/11), cos(4π/11), ±sin(4π/11)),
- (cos(6π/11), ±sin(6π/11), cos(6π/11), ±sin(6π/11)),
- (cos(6π/11), ±sin(6π/11), cos(8π/11), ±sin(8π/11)),
- (cos(6π/11), ±sin(6π/11), cos(10π/11), ±sin(10π/11)),
- (cos(8π/11), ±sin(8π/11), 1, 0),
- (cos(8π/11), ±sin(8π/11), cos(2π/11), ±sin(2π/11)),
- (cos(8π/11), ±sin(8π/11), cos(4π/11), ±sin(4π/11)),
- (cos(8π/11), ±sin(8π/11), cos(6π/11), ±sin(6π/11)),
- (cos(8π/11), ±sin(8π/11), cos(8π/11), ±sin(8π/11)),
- (cos(8π/11), ±sin(8π/11), cos(10π/11), ±sin(10π/11)),
- (cos(10π/11), ±sin(10π/11), 1, 0),
- (cos(10π/11), ±sin(10π/11), cos(2π/11), ±sin(2π/11)),
- (cos(10π/11), ±sin(10π/11), cos(4π/11), ±sin(4π/11)),
- (cos(10π/11), ±sin(10π/11), cos(6π/11), ±sin(6π/11)),
- (cos(10π/11), ±sin(10π/11), cos(8π/11), ±sin(8π/11)),
- (cos(10π/11), ±sin(10π/11), cos(10π/11), ±sin(10π/11)).

## External links[edit | edit source]

- Bowers, Jonathan. "Category A: Duoprisms".