# Decagonal tegum

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Decagonal tegum | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Det |

Coxeter diagram | m2m10o |

Elements | |

Faces | 20 isosceles triangles |

Edges | 10+20 |

Vertices | 2+10 |

Vertex figure | 2 decagons, 10 squares |

Measures (edge length 1) | |

Dihedral angle | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 3 |

Related polytopes | |

Army | Det |

Regiment | Det |

Dual | Decagonal prism |

Conjugate | Decagrammic tegum |

Abstract & topological properties | |

Flag count | 120 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I_{2}(10)×A_{1}, order 40 |

Convex | Yes |

Nature | Tame |

The **decagonal tegum**, also called a **decagonal bipyramid**, is a tegum with a decagon as the midsection, constructed as the dual of a decagonal prism. It has 20 isosceles triangles as faces, with 2 order–10 and 10 order–4 vertices.

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

## External links[edit | edit source]

- Wikipedia contributors. "Decagonal bipyramid".
- Hi.gher.Space Wiki Contributors. "Decagonal bipyramid".