# Dihedron

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n-gonal dihedron | |
---|---|

Rank | 3 |

Type | Regular |

Space | Spherical |

Notation | |

Coxeter diagram | (xno2o) |

Schläfli symbol | {n,2} |

Elements | |

Faces | 2 n-gons |

Edges | n |

Vertices | n |

Vertex figure | Digon |

Measures (edge length 1) | |

Dihedral angle | n-n: 0° |

Central density | 1 |

Related polytopes | |

Army | n-gonal dihedron |

Regiment | n-gonal dihedron |

Dual | n-gonal hosohedron |

Abstract properties | |

Euler characteristic | 2 |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I_{2}(n)×A_{1}, order 4n |

Convex | Yes |

Nature | Tame |

A **dihedron** is a polyhedron made of 2 faces which share all edges. It is degenerate if embedded in 3D Euclidean space, but it can be embedded in 3D spherical space. It can be thought of as a tiling of the sphere.

It is the three-dimensional case of a ditope.

Regular dihedra exist for all regular *n*-gons for *n* ≥ 2. The digonal dihedron, consisting of 2 digonal faces, is also the digonal hosohedron.

## External links[edit | edit source]

- Wikipedia Contributors. "Dihedron".