equilateral polygon

A polygon is equilateral if all of its sides are congruent.

Common examples of equilateral polygons are rhombi and regular polygons such as equilateral triangles and squares.

Let $T$ be a triangle in Euclidean geometry, hyperbolic geometry, or spherical geometry. Then the following are equivalent:

• $T$ is equilateral;

• $T$ is equiangular;

• $T$ is regular.

If $T$ is allowed to be a polygon that has more than three sides, then the above statement is no longer true in any of the indicated geometries.

Below are some pictures of equilateral polygons that are not equiangular.

Title	equilateral polygon
Canonical name	EquilateralPolygon
Date of creation	2013-03-22 17:12:41
Last modified on	2013-03-22 17:12:41
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	10
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 51-00
Synonym	equilateral
Related topic	BasicPolygon