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 polytope providing a technique that allows the abstract regular polytope to be constructed from its symmetry group in a standard and straightforward manner. For examples of polygons in nature, see: Each of the Platonic solids occurs naturally in one form or another: Regular polytope In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or "j"-faces (for all 0 ≤ "j" ≤ "n", where "n" is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries