The Dihedral Group

The dihedral group of order 2n is the symmetry group of a n-sided regular polygon. It is denoted D2n.

The group comprises the identity element e, together with n-1 rotations {R1, R2Rn-1}, and n reflections {M1, M2Mn}. The identity and the rotations form a cyclic sub-group of order n. There are n sub-groups of order 2 each formed by the identity and a single reflection. Additional sub-groups (including more of order 2 and n may be possible depending on the factors of n.

Special Cases: D2 = C2 ; D4 = C2 × C2 .