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
Weitzenböck's inequality that the sum of areas of the equilateral triangles is always greater or equal than the threefold area of the original triangle. This can now can be shown by replicating area of the triangle three times within the equilateral triangles. To achieve that the Fermat point is used to partition the triangle into three obtuse subtriangles with a formula_8 angle and each of those subtriangles is replicated three times within the equilateral triangle next to it. This only works if every angle of the triangle is smaller than formula_8, since otherwise the Fermat point is not located in the interior