 Henagon

Henagon
On a circle, a henagon is a tessellation with a single vertex, and one 360 degree arc.Edges and vertices 1 Schläfli symbol {1} Coxeter–Dynkin diagrams Internal angle (degrees) 360° In geometry a henagon (or monogon) is a polygon with one edge and one vertex. It has Schläfli symbol {1}. Since a henagon has only one side and only one interior angle, every henagon is regular by definition.
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In Euclidean geometry
In Euclidean geometry a henagon is usually considered to be an impossible object, because its endpoints must coincide, unlike any Euclidean line segment. For this reason, most authorities do not consider the henagon as a proper polygon in Euclidean geometry.
In spherical geometry
In spherical geometry, on the other hand, a finite henagon can be drawn by placing a single vertex anywhere on a great circle. Two henagons can be used to construct a dihedron on a sphere, with Schläfli symbol, {1,2}.
The henagon can be used in spherical polyhedra, for example the henagonal dihedron {1, 2}, the digonal hosohedron {2, 1} and the henagonal henahedron {1, 1}. The henagonal henahedron consists of a single vertex, no edges and a single face (the whole sphere minus the vertex.)
See also
References
 Olshevsky, George, Monogon at Glossary for Hyperspace.
 Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955
Regular polygons Listed by number of sides 1–10 sides  Henagon (Monogon)
 Digon
 Equilateral triangle
 Square
 Pentagon
 Hexagon
 Heptagon
 Octagon
 Nonagon (Enneagon)
 Decagon
11–20 sides Others Star polygons This geometryrelated article is a stub. You can help Wikipedia by expanding it.