Definition:Dihedral Group D6
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Example of Dihedral Group
The dihedral group $D_6$ is the symmetry group of the regular hexagon:
Let $\HH = ABCDEF$ be a regular hexagon.
The various symmetry mappings of $\HH$ are:
- The identity mapping $e$
- The rotations through multiples of $60 \degrees$ anticlockwise about the center of $\HH$
- The reflections in the indicated axes.
Let $\alpha$ denote rotation of $\HH$ anticlockwise through $\dfrac \pi 3$ radians ($60 \degrees$).
Let $\beta$ denote reflection of $\HH$ in the $AD$ axis.
The symmetries of $\HH$ form the dihedral group $D_6$.