# Monogon

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

Monogon
On a circle, a monogon is a tessellation with a single vertex, and one 360-degree arc edge.
TypeRegular polygon
Edges and vertices1
Schläfli symbol{1} or h{2}
Coxeter diagram or
Symmetry group[ ], Cs
Dual polygonSelf-dual

## 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.

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