# Enneagon

The **enneagon** sometimes referred to as a **nonagon**, is a polygon with 9 sides. A regular enneagon has equal sides and equal angles.

Enneagon | |
---|---|

Rank | 2 |

Type | Regular |

Notation | |

Bowers style acronym | En |

Coxeter diagram | x9o () |

Schläfli symbol | {9} |

Elements | |

Edges | 9 |

Vertices | 9 |

Vertex figure | Dyad, length |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | 140° |

Central density | 1 |

Number of external pieces | 9 |

Level of complexity | 1 |

Related polytopes | |

Army | En |

Dual | Enneagon |

Conjugates | Enneagram, great enneagram |

Abstract & topological properties | |

Flag count | 18 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(9), order 18 |

Flag orbits | 1 |

Convex | Yes |

Net count | 1 |

Nature | Tame |

Like regular heptagons, regular enneagons are rarely found in higher polytopes that are objects of study, as they do not occur any non-prismatic uniform polyhedra or Johnson solids. A notable exception is the pairwise augmented cupolas, which are acrohedra. Enneagons also appear in some near-miss Johnson solids, such as the sesquitruncated octahedron.

## Naming Edit

The name *enneagon* is derived from the Ancient Greek *ἐννέα* (9) and *γωνία* (angle), referring to the number of vertices.

Other names include:

**En**, Bowers style acronym, short for "enneagon".

The combining prefix in BSAs is **e-**, as in **e**dip.

## Vertex coordinates Edit

Coordinates for an enneagon of edge length , centered at the origin, are:

- ,
- ,
- ,
- ,
- .

## Variations Edit

Besides the regular enneagon, other enneagons with triangular, mirror, or no symmetry exist. A few higher polytopes, such as certain swirlchora, have trigon-symmetric enneagons as faces.

## Stellations Edit

- 1st stellation: Enneagram
- 2nd stellation: Fissal enneagram
*(compound of three triangles)* - 3rd stellation: Great enneagram

## External links Edit

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

- Wikipedia contributors. "Nonagon".