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Monogon  

On a circle, a monogon is a tessellation with a single vertex, and one 360degree arc edge.


Type  Regular polygon 
Edges and vertices  1 
Schläfli symbol  {1} or h{2} 
Coxeter diagram  or 
Symmetry group  [ ], C_{s} 
Dual polygon  Selfdual 
In geometry a monogon is a polygon with one edge and one vertex. It has Schläfli symbol {1}.^{[1]} Since a monogon has only one side and only one vertex, every monogon is regular by definition.
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, 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.^{[1]}
Monogonal dihedron, {1,2} 
Monogonal hosohedron, {2,1} 
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