Equilateral polygon


In geometry, three or more than three straight lines make a polygon and an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it doesn’t need to be equiangular, but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon doesn’t need to be a convex polygon: it could be concave or even self-intersecting.

Examples

All regular polygons and isotoxal polygons are equilateral.
An equilateral triangle is a regular triangle 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 is a regular polygon.
A tangential polygon is equilateral if and only if the alternate angles are equal. Thus if the number of sides n is odd, a tangential polygon is equilateral if and only if it is regular.
Viviani's theorem generalizes to equilateral polygons: The sum of the perpendicular distances from an interior point to the sides of an equilateral polygon is independent of the location of the interior point.
The principal diagonals of a hexagon each divide the hexagon into quadrilaterals. In any convex equilateral hexagon with common side a, there exists a principal diagonal d1 such that
and a principal diagonal d2 such that

Triambi

Triambi are equilateral hexagons with trigonal symmetry: