# Enneagonal antiprism

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Enneagonal antiprism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Eap |

Coxeter diagram | s2s18o |

Conway notation | A9 |

Elements | |

Faces | 18 triangles, 2 enneagons |

Edges | 18+18 |

Vertices | 18 |

Vertex figure | Isosceles trapezoid, edge lengths 1, 1, 1, 2cos(π/9) |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–3: |

9–3: | |

Height | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 4 |

Related polytopes | |

Army | Eap |

Regiment | Eap |

Dual | Enneagonal antitegum |

Conjugate | Great enneagrammic retroprism |

Abstract & topological properties | |

Flag count | 144 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (I_{2}(18)×A_{1})/2, order 36 |

Convex | Yes |

Nature | Tame |

The **enneagonal antiprism**, or **eap**, is a prismatic uniform polyhedron. It consists of 18 triangles and 2 enneagons. Each vertex joins one enneagon and three triangles. As the name suggests, it is an antiprism based on an enneagon.

## Vertex coordinates[edit | edit source]

The vertices of an enneagonal antiprism, centered at the origin and with edge length 2sin(π/9), are given by the following points, as well as their central inversions:

where

## External links[edit | edit source]

- Wikipedia contributors. "Enneagonal antiprism".