Monogon

In geometry, a monogon is a curve, considered by some as a polygon with one edge and one vertex. It has Schläfli symbol {1}.^[1]

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, 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]

• Digon

• Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955