monogon
{{short description|Polygon with one edge and one vertex}}
{{Infobox polygon
| 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
| euler =
| edges = 1
| schläfli = {1} or h{2}
| wythoff =
| coxeter = {{CDD|node}} or {{CDD|node_h|2x|node}}
| symmetry = [ ], Cs
| area =
| angle =
| dual = Self-dual
| properties = }}
In geometry, a monogon, also known as a henagon, is a polygon with one edge and one vertex. It has Schläfli symbol {1}.Coxeter, Introduction to geometry, 1969, Second edition, sec 21.3 Regular maps, p. 386-388
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.
| class=wikitable |
| align=center
|160px |160px |
See also
{{wiktionary|monogon}}
References
{{reflist}}
- 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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{{polygons}}
{{polyhedra}}