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 $\mathcal H = ABCDEF$ be a regular hexagon.

SymmetryGroupRegularHexagon.png

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

The identity mapping $e$
The rotations through multiples of $60 \degrees$
The reflections in the indicated axes.

Let $\alpha$ denote rotation of $\mathcal H$ anticlockwise through $\dfrac \pi 3$ radians ($60 \degrees$).

Let $\beta$ denote reflection of $\mathcal H$ in the $AD$ axis.


The symmetries of $\mathcal H$ form the dihedral group $D_6$.


Matrix Representations

Dihedral Group D6/Matrix Representation