Monogon

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–Dynkin diagrams	or
Symmetry group	[ ], Cs
Dual polygon	Self-dual

In geometry, a monogon, also known as a henagon, is a polygon with one edge and one vertex. It has Schläfli symbol {1}.^[1]

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° lune face, and one edge (meridian) between the two vertices.^[1]

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

References

^ ^a ^b Coxeter, Introduction to geometry, 1969, Second edition, sec 21.3 Regular maps, p. 386-388

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