Dihedral Group/Examples/D1

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Example of Dihedral Group

The dihedral group $D_1$ is the symmetry group of the line segment:

Let $\triangle AB$ be a line segment.

SymmetryGroupLineSegment.png

The various symmetry mappings of $AB$ are:

The identity mapping $e$
The rotation $r$ of $180^\circ$ about the center of $AB$.

This group is known as the symmetry group of the line segment.