Regular polygon Regular polygon In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed. "These properties apply to all regular polygons, whether convex or star." A regular "n"-sided polygon has rotational symmetry of order "n". All vertices of a regular
Regular polygon edges and faces in orthogonal projections "m"-cubes. In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. The list gives the number of solutions for smaller polygons. The area "A" of a convex regular "n"-sided polygon having side "s", circumradius "R", apothem "a", and perimeter "p" is given by For regular polygons with side "s" = 1, circumradius "R" = 1, or apothem "a" = 1, this produces the following table: (Note that since formula_11 as formula_12, the area when formula_13 is tending to formula_14 as formula_15 grows large.) Of