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 [ ], Cs
Dual polygon Self-dual

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.

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} Look up monogon in Wiktionary, the free dictionary.