Monogon
Monogon | |
---|---|
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
[edit]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
[edit]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} |
See also
[edit]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
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By number of sides |
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Classes |
Listed by number of faces and type | |
1–10 faces | |
11–20 faces | |
>20 faces |
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elemental things |
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convex polyhedron |
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non-convex polyhedron |
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prismatoids |
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