= Symmetry group of a square
{title2=$D_4=\langle r,s\mid r^4=s^2=e,\ srs=r^{-1}\rangle$}
Take $r$ as a counterclockwise quarter-turn and $s$ as reflection across the horizontal axis. The eight <symmetries> of a square are $e,r,r^2,r^3,s,rs,r^2s,r^3s$. The last four are reflections across the horizontal axis, the diagonal $y=x$, the vertical axis and the diagonal $y=-x$, respectively. This is a <dihedral group> of order eight; the subscript convention $D_4$ counts polygon vertices, while some authors use $D_8$ for the same <group>.
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