A regular polygon is a two-dimensional geometric figure that has equal sides and equal angles. In Euclidean geometry, a regular polygon is both direct equiangular and equilateral, meaning all angles are equal in measure, and all sides have the same length
. Regular polygons can be either convex, star, or skew
. Some examples of regular polygons include the equilateral triangle, square, regular pentagon, and regular hexagon
. Properties of regular polygons include:
- All sides are equal in length
- All interior angles are equal and measure 360∘n\frac{360^\circ}{n}n360∘, where n is the number of sides
- The sum of the interior angles of a regular polygon is always 180∘180^\circ 180∘
- Regular polygons can be constructed with compass and straightedge if and only if the odd prime factors of n are distinct Fermat primes
Regular polygons are used in various fields, such as mathematics, art, and architecture, due to their aesthetically pleasing properties and mathematical structure.
