# Hexagonal-hendecagonal duoprism

(Redirected from 6-11 duoprism)

Jump to navigation
Jump to search
Hexagonal-hendecagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Hahendip |

Info | |

Coxeter diagram | x6o x11o |

Symmetry | G2×I2(11), order 264 |

Army | Hahendip |

Regiment | Hahendip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths √3 (base 1), 2cos(π/11) (base 2), and √2 (sides) |

Cells | 11 hexagonal prisms, 6 hendecagonal prisms |

Faces | 66 squares, 11 hexagons, 6 hendecagons |

Edges | 66+66 |

Vertices | 66 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Hip–6–hip: |

Henp–11–Henp: 120° | |

Hip–4–henp: 90° | |

Central density | 1 |

Euler characteristic | 0 |

Number of pieces | 17 |

Level of complexity | 6 |

Related polytopes | |

Dual | Hexagonal-hendecagonal duotegum |

Conjugates | Hexagonal-small hendecagrammic duoprism, Hexagonal-hendecagrammic duoprism, Hexagonal-great hendecagrammic duoprism, Hexagonal-grand hendecagrammic duoprism |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **hexagonal-hendecagonal duoprism** or **hahendip**, also known as the **6-11 duoprism**, is a uniform duoprism that consists of 6 hendecagonal prisms and 11 hexagonal prisms, with two of each joining at each vertex.

## Vertex coordinates[edit | edit source]

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

- (±2sin(π/11), 0, 1, 0),
- (±2sin(π/11), 0, cos(2π/11), ±sin(2π/11)),
- (±2sin(π/11), 0, cos(4π/11), ±sin(4π/11)),
- (±2sin(π/11), 0, cos(6π/11), ±sin(6π/11)),
- (±2sin(π/11), 0, cos(8π/11), ±sin(8π/11)),
- (±2sin(π/11), 0, cos(10π/11), ±sin(10π/11)),
- (±sin(π/11), ±sin(π/11)√3, 1, 0),
- (±sin(π/11), ±sin(π/11)√3, cos(2π/11), ±sin(2π/11)),
- (±sin(π/11), ±sin(π/11)√3, cos(4π/11), ±sin(4π/11)),
- (±sin(π/11), ±sin(π/11)√3, cos(6π/11), ±sin(6π/11)),
- (±sin(π/11), ±sin(π/11)√3, cos(8π/11), ±sin(8π/11)),
- (±sin(π/11), ±sin(π/11)√3, cos(10π/11), ±sin(10π/11)).

## Representations[edit | edit source]

A hexagonal-hendecagonal duoprism has the following Coxeter diagrams:

- x6o x11o (full symmetry)
- x3x x11o (hexagons as ditrigons)

## External links[edit | edit source]

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