Symmetry Group of Line Segment/Cayley Table

Cayley Table of Symmetry Group of Line Segment

The Cayley table of the symmetry group of the line segment can be written:

$\begin{array}{c|cccccc}

 & e & r \\

\hline e & e & r \\ r & r & e \\ \end{array}$

where:

$e$ is the identity mapping

$r$ is the plane rotation of $180^\circ$ about the midpoint of $AB$.