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Example of Dihedral Group
The dihedral group $D_2$ is the symmetry group of the rectangle:
Let $\RR = ABCD$ be a (non-square) rectangle.
The various symmetry mappings of $\RR$ are:
- The identity mapping $e$
- The rotation $r$ (in either direction) of $180^\circ$
- The reflections $h$ and $v$ in the indicated axes.
The symmetries of $\RR$ form the dihedral group $D_2$.