Polygon with one edge. And one vertex
| Monogon | |
|---|---|
 On a circle, a monogon is: a tessellation with a single vertex. And one 360-degree arc edge. | |
| Type | Regular polygon |
| Edges and vertices | 1 |
| Schläfli symbol | {1}/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}.
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."
 Monogonal dihedron, {1,2} |
 Monogonal hosohedron, {2,1} |
See also※
References※
- 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