# Monogon

Monogon | |
---|---|

On a circle, a monogon is a tessellation with a single vertex, and one 360-degree arc edge. | |

Type | Regular polygon |

Edges and vertices | 1 |

Schläfli symbol | {1} or h{2} |

Coxeter diagram | or |

Symmetry group |
[ ], C_{s} |

Dual polygon | Self-dual |

In geometry a **monogon** is a polygon with one edge and one vertex. It has Schläfli symbol {1}.^{[1]} Since a monogon has only one side and only one vertex, every monogon is regular by definition.

## In Euclidean geometry

In Euclidean geometry a *monogon* is a degenerate polygon because its endpoints must coincide, unlike any Euclidean line segment. Most definitions of a polygon in Euclidean geometry do not admit the monogon.

## In spherical geometry

In spherical geometry, a monogon can be constructed as a vertex on a great circle (equator). This forms a dihedron, {1,2}, with two hemispherical monogonal faces which share one 360° edge and one vertex. Its dual, a hosohedron, {2,1} has two antipodal vertices at the poles, one 360 degree lune face, and one edge (meridian) between the two vertices.^{[1]}

Monogonal dihedron, {1,2} |
Monogonal hosohedron, {2,1} |

## See also

Look up in Wiktionary, the free dictionary.monogon |

## References

- Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955
- Coxeter, H.S.M;
*Regular Polytopes*(third edition). Dover Publications Inc. ISBN 0-486-61480-8