In geometry, a monogon, also known as a henagon, is a polygon with one edge and one vertex. It has Schläfli symbol {1}.[1]
Monogon | |
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![]() On a circle, a monogon is a tessellation with a single vertex, and one 360-degree arc edge. | |
Typ | Regular polygon |
Edges and vertices | 1 |
Schläfli symbol | {1} or h{2} |
Coxeter–Dynkin diagrams | ![]() ![]() ![]() ![]() |
Symmetry group | [ ], Cs |
Dual polygon | Self-dual |
In Euclidean geometry
editIn 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
editIn 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} |
See also
editLook up monogon in Wiktionary, the free dictionary.
References
edit- 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