Definition:Symmetry Group of Regular Hexagon

Group Example
Let $\HH = ABCDEF$ be a regular hexagon.


 * SymmetryGroupRegularHexagon.png

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 $D_6$.