Monogon

Monogon
On a circle, amonogonis atessellationwith a single vertex, and one 360-degree arc edge.
Type	Regular polygon
Edgesandvertices	1
Schläfli symbol	{1} orh{2}
Coxeter–Dynkin diagrams	or
Symmetry group	[ ], Cs
Dual polygon	Self-dual

Ingeometry,amonogon,also known as ahenagon,is apolygonwith oneedgeand onevertex.It hasSchläfli symbol{1}.

In Euclidean geometry

InEuclidean geometryamonogonis adegeneratepolygon 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

Inspherical geometry,a monogon can be constructed as a vertex on agreat circle(equator). This forms adihedron,{1,2}, with twohemisphericalmonogonal faces which share one 360° edge and one vertex. Its dual, ahosohedron,{2,1} has twoantipodalvertices at the poles, one 360°luneface, and one edge (meridian) between the two vertices.

Monogonaldihedron,{1,2}

Monogonalhosohedron,{2,1}

See also

• Digon

References

• Herbert Busemann,The geometry of geodesics. New York, Academic Press, 1955
• Coxeter, H.S.M;Regular Polytopes(third edition). Dover Publications Inc.ISBN0-486-61480-8