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Monogon

Polygon with one edge and one vertex

Summary

Polygon with one edge and one vertex

Field	Value
name	Monogon
image	Monogon.svg
caption	On a circle, a monogon is a tessellation with a single vertex, and one 360-degree arc edge.
type	Regular polygon
edges	1
schläfli	{1} or h{2}
coxeter	or
symmetry	[ ], Cs
dual	Self-dual

In geometry, a monogon, also known as a henagon, is a curve, considered by some as 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.

[[File:Hengonal dihedron.png	160px]]Monogonal dihedron, {1,2}	[[File:Henagonal hosohedron.png	160px]]Monogonal hosohedron, {2,1}

References

Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955
Coxeter, H.S.M; Regular Polytopes (third edition). Dover Publications Inc.

References

Coxeter, ''Introduction to geometry'', 1969, Second edition, sec 21.3 ''Regular maps'', p. 386-388

Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

polygons-by-the-number-of-sides 1-(number)

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