# Hexagonal tegum

The **hexagonal tegum**, also called a **hexagonal bipyramid**, is a tegum with a hexagon as the midsection, constructed as the dual of a hexagonal prism. It has 12 isosceles triangles as faces, with 2 order–6 and 6 order–4 vertices. The variant with equilateral triangles is flat, and is not considered to be a Johnson solid.

Hexagonal tegum | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Hat |

Coxeter diagram | m2m6o |

Elements | |

Faces | 12 isosceles triangles |

Edges | 6+12 |

Vertices | 2+6 |

Vertex figure | 2 hexagons, 6 squares |

Measures (edge lengths 1, ) | |

Dihedral angle | |

Central density | 1 |

Number of external pieces | 12 |

Level of complexity | 3 |

Related polytopes | |

Army | Hat |

Regiment | Hat |

Dual | Hexagonal prism |

Conjugate | Hexagonal tegum |

Abstract & topological properties | |

Flag count | 72 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | G_{2}×A_{1}, order 24 |

Convex | Yes |

Nature | Tame |

In the variant obtained as the dual of a uniform hexagonal prism, the side edges are exactly 2 times the length of the edges of the base hexagon. Each face has apex angle and base angles . If the base hexagon has edge length 1, its height is .

## External links edit

- Wikipedia contributors. "Hexagonal bipyramid".
- McCooey, David. "Hexagonal Dipyramid"
- Hi.gher.Space Wiki Contributors. "Hexagonal bipyramid".