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\begin{center} {\Large\bf The Dihedral Group $D_{2n}$}
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\noi {\tt Notation:} $Z_n$ is the integers $\{0,\ldots,n-1\}$ under addition mod $n$.
The Dihedral Group $D_{2n}$ is the group of symmetries of the regular
$n$-gon. We imagine the vertices of the regular $n$-gon labelled
$0,1,\ldots,n-1$ in counterclockwise direction.
In these notes we assume $n$ is {\em odd}. The case $n$ even
is also interesting but has differences.
The symmetries come in three forms:
\ben
\item $R^i$, $1\leq i < n$. This is a rotation by $i$ notches.
As a map from the vertices to themselves it moves a vertex up
$i$ notches so we write $x\ra x+i$ where $+$ is in $Z_n$. Note
that the inverse of $R^i$ is $R^{n-i}$ which we can also write
$R^{-i}$.
\item $F_i$, $0\leq i