# Enneagonal tegum

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Enneagonal tegum | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Et |

Coxeter diagram | m2m9o () |

Elements | |

Faces | 18 isosceles triangles |

Edges | 9+18 |

Vertices | 2+9 |

Vertex figure | 2 enneagons, 9 squares |

Measures (edge length 1) | |

Dihedral angle | |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 3 |

Related polytopes | |

Army | Et |

Regiment | Et |

Dual | Enneagonal prism |

Conjugates | Enneagrammic tegum, Great enneagrammic tegum |

Abstract & topological properties | |

Flag count | 108 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I_{2}(9)×A_{1}, order 36 |

Convex | Yes |

Nature | Tame |

The **enneagonal tegum**, also called an **enneagonal bipyramid**, is a tegum with an enneagon as the midsection, constructed as the dual of an enneagonal prism. It has 18 isosceles triangles as faces, with 2 order–9 and 9 order–4 vertices. .

In the variant obtained as the dual of a uniform enneagonal prism, the side edges are times the length of the edges of the base enneagon. Each face has apex angle and base angles . If the base enneagon has edge length 1, its height is .