Dihedral Group/Examples/D2

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Example of Dihedral Group

The dihedral group $D_2$ is the symmetry group of the rectangle:

Let $\mathcal R = ABCD$ be a (non-square) rectangle.

SymmetryGroupRectangle.png

The various symmetry mappings of $\mathcal R$ are:

The identity mapping $e$
The rotation $r$ (in either direction) of $180^\circ$
The reflections $h$ and $v$ in the indicated axes.