# Hendecagrammic duoprism

Hendecagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Info | |

Coxeter diagram | x11/3o x11/3o |

Symmetry | I2(11)≀S2, order 968 |

Army | Handip |

Elements | |

Vertex figure | Tetragonal disphenoid, edge lengths 2cos(3π/11) (bases) and √2 (sides) |

Cells | 22 hendecagrammic prisms |

Faces | 22 hendecagrams, 121 squares |

Edges | 242 |

Vertices | 121 |

Measures (edge length 1) | |

Circumradius | √2/(2sin(3π/11)) ≈ 0.93564 |

Inradius | 1/(2tan(3π/11)) ≈ 0.43325 |

Hypervolume | 121/(16tan^{2}(3π/11)) ≈ 5.67816 |

Dichoral angles | 11/3p–11/3–11/3p: 5π/11 ≈ 81.81818° |

11/3p–4–11/3p: 90° | |

Related polytopes | |

Dual | Hendecagrammic duotegum |

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

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **hendecagrammic duoprism**, also known as the **hendecagrammic-hendecagrammic duoprism**, the **11/3 duoprism** or the **11/3-11/3 duoprism**, is a noble uniform duoprism that consists of 22 hendecagrammic prisms and 121 vertices.

The name can also refer to the small hendecagrammic duoprism, the small hendecagrammic-hendecagrammic duoprism, the small hendecagrammic-great hendecagrammic duoprism, the small hendecagrammic-grand hendecagrammic duoprism, the hendecagrammic-great hendecagrammic duoprism, the hendecagrammic-grand hendecagrammic duoprism, the great hendecagrammic duoprism, the great hendecagrammic-grand hendecagrammic duoprism, or the grand hendecagrammic duoprism.

## Vertex coordinates[edit | edit source]

The vertex coordinates of a hendecagrammic duoprism, centered at the origin and with edge length 2sin(3π/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".

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