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 $AB$ be a line segment.

Symmetry-Group-of-Line-Segment.png

The symmetry mappings of $AB$ are:

The identity mapping $e$
The rotation $r$ of $180 \degrees$ about the midpoint of $AB$.

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