Dihedral group

The dihedral groups $D_{2n}$ are an infinite family of groups which are in general noncommutative. Each dihedral group $D_{2n}$ is defined to be the group of linear symmetries of a regular $n$-gon.


  • The order of $D_{2n}$ is $2n$.
  • The group $D_{2n}$ has a presentation in the form $\langle r, s\mid r^n = 1, s^2 = 1, srs = r^{-1}\rangle$.
  • For $n > 3$, $D_{2n}$ is noncommutative.

See also