# Digon

Digon | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Coxeter diagram | x2o () |

Schläfli symbol | {2} |

Elements | |

Edges | 2 |

Vertices | 2 |

Vertex figure | Dyad, length 0 |

Measures (edge length 1) | |

Angle | 0° |

Central density | 1 |

Related polytopes | |

Army | Digon |

Dual | Digon |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | K_{2}, order 4 |

Convex | Yes |

A **digon** is a polygon with two sides. It is degenerate if embedded in Euclidean space, as its edges coincide. It can however be thought of as a tiling of the circle. In two-dimensional or higher spherical space, it can form a lune such as the ones making up a hosohedron.

In Euclidean space, a convex n -gon can be formed as the intersection of n half-planes, so one possible realization of a Euclidean digon is as the intersection of two parallel half-planes, forming an infinite "stripe" with two ideal vertices.

It is the only rank 2 ditope and hosotope. It is also the two-dimensional demihypercube.

The digon is the only non-lattice polygon and the simplest non-lattice polytope. In turn, many (though not all) non-lattice polytopes contain digonal sections.

The digon is the simplest possible polygon, as monogons are disallowed under almost all definitions of a polytope. Despite this, it may be built as the omnitruncate of a (generalized) complex with two flags and two flag-changes between them. As such, this complex is called the monogonal complex.

## External links[edit | edit source]