# Symmetry Group of Equilateral Triangle/Cayley Table

## Cayley Table of Symmetry Group of Equilateral Triangle

The Cayley table of the symmetry group of the equilateral triangle can be written:

$\begin{array}{c|ccc|ccc} \circ & e & p & q & r & s & t \\ \hline e & e & p & q & r & s & t \\ p & p & q & e & s & t & r \\ q & q & e & p & t & r & s \\ \hline r & r & t & s & e & q & p \\ s & s & r & t & p & e & q \\ t & t & s & r & q & p & e \\ \end{array}$

where:

 $\displaystyle e$ $:$ $\displaystyle (A) (B) (C)$ Identity mapping $\displaystyle p$ $:$ $\displaystyle (ABC)$ Rotation of $120 \degrees$ anticlockwise about center $\displaystyle q$ $:$ $\displaystyle (ACB)$ Rotation of $120 \degrees$ clockwise about center $\displaystyle r$ $:$ $\displaystyle (BC)$ Reflection in line $r$ $\displaystyle s$ $:$ $\displaystyle (AC)$ Reflection in line $s$ $\displaystyle t$ $:$ $\displaystyle (AB)$ Reflection in line $t$