Monogon

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

Template:Short description Template:Infobox polygon 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

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.[1]

File:Hengonal dihedron.png
Monogonal dihedron, {1,2}
File:Henagonal hosohedron.png
Monogonal hosohedron, {2,1}

See also

Template:Sister project

References

<templatestyles src="Reflist/styles.css" />

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

Script error: No such module "Check for unknown parameters".

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

Script error: No such module "Navbox". Script error: No such module "Navbox".