# Hendecagon

Hendecagon | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Heng |

Coxeter diagram | x11o () |

Schläfli symbol | {11} |

Elements | |

Edges | 11 |

Vertices | 11 |

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

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | |

Central density | 1 |

Number of pieces | 11 |

Level of complexity | 1 |

Related polytopes | |

Army | Heng |

Dual | Hendecagon |

Conjugates | Small hendecagram, hendecagram, great hendecagram, grand hendecagram |

Abstract properties | |

Flag count | 22 |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **hendecagon** is a polygon with 11 sides. A regular hendecagon has equal sides and equal angles.

The combining prefix in BSAs is **hen-**, as in hentet, or **han-**, as in handip.

It has four stellations, these being the small hendecagram, the hendecagram, the great hendecagram, and the grand hendecagram.

It is the smallest regular convex polygon that cannot form a planar vertex with only other regular convex polygons.

Higher polytopes containing regular hendecagons that are "interesting" in some sense are rare. An exception is three members of the family of pairwise augmented cupolae, which are 11-4-3 acrohedra (all faces are regular).

## Naming[edit | edit source]

The name *hendecagon* is derived from the Ancient Greek *ἕνδεκα* (11) and *γωνία* (angle), referring to the number of vertices.

Other names include:

**heng**, Bowers style acronym, short for "hendecagon"

## Vertex coordinates[edit | edit source]

Vertex coordinates for a hendecagon of edge length , centered at the origin, are:

- ,
- ,
- ,
- ,
- ,
- .

## External links[edit | edit source]

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

- Wikipedia Contributors. "Hendecagon".