# Grand hendecagram

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Grand hendecagram | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Gahn |

Coxeter diagram | x11/5o () |

Schläfli symbol | {11/5} |

Elements | |

Edges | 11 |

Vertices | 11 |

Vertex figure | Dyad, length 2cos(5π/11) |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | |

Central density | 5 |

Number of external pieces | 22 |

Level of complexity | 2 |

Related polytopes | |

Army | Heng, edge length |

Dual | Grand hendecagram |

Conjugates | Hendecagon, small hendecagram, hendecagram, great hendecagram |

Convex core | Hendecagon |

Abstract & topological properties | |

Flag count | 22 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(11), order 22 |

Convex | No |

Nature | Tame |

The **grand hendecagram** is a non-convex polygon with 11 sides. It's created by taking the fourth stellation of a hendecagon. A regular grand hendecagram has equal sides and equal angles.

It is one of four regular 11-sided star polygons, the other three being the small hendecagram, the hendecagram, and the great hendecagram.

## Vertex coordinates[edit | edit source]

Coordinates for a grand hendecagram of edge length 2sin(5π/11), centered at the origin, are:

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

## External links[edit | edit source]

- Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".

- Wikipedia Contributors. "Hendecagram".