The general dihedral group Dn is the symmetry group of the regular n-sided polygon and consists of the identity transformation, rotation about the axis through the center of the polygon, and reflection through each of the polygon's mirror planes (these planes always contain the axis of rotation and either a vertex or the center of a side). An n-sided regular polygon will always have n planes of reflection. An equilateral triangle will have the symmetry group D3, a square D4, a pentagon D5, etc. In each of these cases, the dihedral groups will contain the subgroups of the polygon's other symmetries. For example, the symmetry group D3 contains the subgroup of C3 (the rotational symmetry) and three second order subgroups (C2 - reflections through each mirror plane).
Page author: Sasie Sealy