Regular polygon facts for kids

Regular polygon with n = 5: pentagon with side s, circumradius R and apothem a

Square diagonals

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.

General properties

Regular convex and star polygons with 3 to 12 vertices labelled with their Schläfli symbols

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 polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon.

Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint. Thus a regular polygon is a tangential polygon.

A regular n-sided polygon can be constructed with compass and straightedge if and only if the odd prime factors of n are distinct Fermat primes. See constructible polygon.

Images for kids

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  Comparison of sizes of regular polygons with the same edge length, from three to sixty sides. The size increases without bound as the number of sides approaches infinity.

See also

In Spanish: Polígono regular para niños