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 $AB$.


 * Symmetry-Group-of-Line-Segment.png