Equilateral polygon with 60° internal angles. An equilateral quadrilateral is called a rhombus, an isotoxal polygon described by an angle α. It includes the square as a special case. A convex equilateral pentagon can be described by two angles α and β, which together determine the other angles. Concave equilateral pentagons exist, as do concave equilateral polygons with any larger number of sides. An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon (a polygon that is both equilateral and equiangular). A tangential polygon (one that has an incircle tangent to all its sides) is equilateral
Equilateral triangle root formula_33 of 1 the triangle is equilateral if and only if Given a point "P" in the interior of an equilateral triangle, the ratio of the sum of its distances from the vertices to the sum of its distances from the sides is greater than or equal to 2, equality holding when "P" is the centroid. In no other triangle is there a point for which this ratio is as small as 2. This is the Erdős–Mordell inequality; a stronger variant of it is Barrow's inequality, which replaces the perpendicular distances to the sides with the distances from "P"