High Quality Content by WIKIPEDIA articles! A regular polygon is a polygon which is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be convex or star. The symmetry group of an n-sided regular polygon is dihedral group Dn (of order 2n): D2, D3, D4,... It consists of the rotations in Cn, together with reflection symmetry in n axes that pass through the center. If n is even then half of these axes pass through two opposite vertices, and the other half through the midpoint of opposite sides. If n is odd then all axes pass through a vertex and the midpoint of the opposite side.