# Hendecagrammic prism

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Hendecagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Info | |

Coxeter diagram | x x11/3o |

Symmetry | I2(11)×A1, order 44 |

Army | Semi-uniform hendecagonal prism |

Regiment | Hendecagrammic prism |

Elements | |

Vertex figure | Isosceles triangle, edge lengths √2, √2, 2cos(3π/11) |

Faces | 11 squares, 2 hendecagrams |

Edges | 11+22 |

Vertices | 22 |

Measures (edge length 1) | |

Circumradius | √1+1/sin^{2}(3π/11)/2 ≈ 0.82928 |

Volume | 11/(4tan(3π/11)) ≈ 2.38289 |

Dihedral angles | 4–11/3: 90° |

4–4: 5π/11 ≈ 81.81818° | |

Height | 1 |

Central density | 3 |

Euler characteristic | 2 |

Related polytopes | |

Dual | Hendecagrammic bipyramid |

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

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **hendecagrammic prism** is a prismatic uniform polyhedron. It consists of 2 hendecagrams and 11 squares. Each vertex joins one hendecagram and two squares. As the name suggests, it is a prism based on a hendecagram.

## Vertex coordinates[edit | edit source]

The coordinates of a hendecagrammic prism, centered at the origin and with edge length 2sin(3π/11), are given by:

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