In geometry, a monogon is a curve, considered by some as a polygon with one edge and one vertex. It has Schläfli symbol {1}.Coxeter, Introduction to geometry, 1969, Second edition, sec 21.3 Regular maps, p. 386-388
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.
Monogonal dihedron, {1,2}Monogonal hosohedron, {2,1}
See also
Digon
References
Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955