Definition:Symmetry Group of Parallelogram

Group Example
Let $\mathcal P = ABCD$ be a (non-rectangular) parallelogram.


 * SymmetryGroupParallelogram.png

The various symmetry mappings of $\mathcal P$ are:
 * The identity mapping $e$
 * The rotation $r$ (in either direction) of $180^\circ$.

The symmetries of $\mathcal P$ form the dihedral group $D_1$.