|bgcolor=#e7dcc3|Internal angle sum||
|bgcolor=#e7dcc3|Inscribed circle diameter||
|bgcolor=#e7dcc3|Circumscribed circle diameter
|bgcolor=#e7dcc3|Properties||convex, cyclic, equilateral, isogonal, isotoxal
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 convex or star. In the limit, a sequence of regular polygons with an increasing number of sides becomes a circle, if the perimeter is fixed, or a regular apeirogon, 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 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.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』