User:Double sharp/List of polygons

1–10 sides

Henagon (1-gon)

Main article: Henagon

On a circle, a henagon is a tessellation with a single vertex, and one 360-degree arc.

Henagonal dihedron

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 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. However, in spherical geometry, a finite henagon can be drawn by placing a single vertex anywhere on a great circle. Two spherical henagons can be used to construct the henagonal 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.)

Digon (2-gon)

Main article: Digon

On a circle, a nondegenerate antipodal digon is a tessellation composed of two vertices and two 180-degree arcs.

In geometry, a digon or 2-gon is a polygon with two sides (edges) and two vertices. It has Schläfli symbol {2}. A digon must be regular because its two edges are the same length. It is degenerate in a Euclidean space, but may be non-degenerate in a spherical space. Some authorities do not consider the digon to be a proper polygon because of its degeneracy in the Euclidean case.