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.

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}.

Henagonal dihedron (up-arrow represents vertex).

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

• Regular polygon
• Digon
• Degeneracy (mathematics)

References

• Olshevsky, George, Monogon at Glossary for Hyperspace.
• Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955

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