# Hexagonal-grand hendecagrammic duoprism

(Redirected from 6-11/5 duoprism)

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Hexagonal-grand hendecagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Info | |

Coxeter diagram | x6o x11/5o |

Symmetry | G2×I2(11), order 264 |

Army | Semi-uniform hahendip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths √3 (base 1), 2cos(5π/11) (base 2), √2 (sides) |

Cells | 11 hexagonal prisms, 6 grand hendecagrammic prisms |

Faces | 66 squares, 11 hexagons, 6 grand hendecagrams |

Edges | 66+66 |

Vertices | 66 |

Measures (edge length 1) | |

Circumradius | √4+csc^{2}(5π/11)/2 ≈ 1.12034 |

Hypervolume | |

Dichoral angles | Hip–6–hip: π/11 ≈ 16.36364° |

11/5p–11/5–11/5p: 120° | |

Hip–4–11/5p: 90° | |

Central density | 5 |

Related polytopes | |

Dual | Hexagonal-grand hendecagrammic duotegum |

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

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **hexagonal-grand hendecagrammic duoprism**, also known as the **6-11/5 duoprism**, is a uniform duoprism that consists of 11 hexagonal prisms and 6 grand hendecagrammic prisms, with 2 of each meeting at each vertex.

## Vertex coordinates[edit | edit source]

The coordinates of a hexagonal-grand hendecagrammic duoprism, centered at the origin and with edge length 2sin(5π/11), are given by:

- (±2sin(5π/11), 0, 1, 0),
- (±2sin(5π/11), 0, cos(2π/11), ±sin(2π/11)),
- (±2sin(5π/11), 0, cos(4π/11), ±sin(4π/11)),
- (±2sin(5π/11), 0, cos(6π/11), ±sin(6π/11)),
- (±2sin(5π/11), 0, cos(8π/11), ±sin(8π/11)),
- (±2sin(5π/11), 0, cos(10π/11), ±sin(10π/11)),
- (±sin(5π/11), ±sin(5π/11)√3, 1, 0),
- (±sin(5π/11), ±sin(5π/11)√3, cos(2π/11), ±sin(2π/11)),
- (±sin(5π/11), ±sin(5π/11)√3, cos(4π/11), ±sin(4π/11)),
- (±sin(5π/11), ±sin(5π/11)√3, cos(6π/11), ±sin(6π/11)),
- (±sin(5π/11), ±sin(5π/11)√3, cos(8π/11), ±sin(8π/11)),
- (±sin(5π/11), ±sin(5π/11)√3, cos(10π/11), ±sin(10π/11)).

## External links[edit | edit source]

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

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