In geometry, a monogon, also known as a henagon, is a polygon with one edge and one vertex. It has Schläfli symbol {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. See also Digon References Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955 Coxeter, H.S.M; Regular Polytopes (third edition). Dover Publications Inc. Polygons by the number of sides 1 (number)