Type Regular polygon Schläfli symbol {1} or h{2} Symmetry group [ ], Cs | Edges and vertices 1 Coxeter diagram or Dual polygon Self-dual | |
In geometry a monogon is a polygon with one edge and one vertex. It has Schläfli symbol {1}. Since a monogon has only one side and only one vertex, every monogon is regular by definition.
Contents
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 degree lune face, and one edge (meridian) between the two vertices.
References
Monogon Wikipedia(Text) CC BY-SA