# Enneagon

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 |

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

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 | edit source]

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 | edit source]

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

- ,
- ,
- ,
- ,
- .

## Variations[edit | edit source]

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 | edit source]

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

## External links[edit | edit source]

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

- Wikipedia contributors. "Nonagon".