# The Dihedral Group

The dihedral group of order 2`n`
is the symmetry group of a
`n`-sided regular polygon.
It is denoted `D`_{2n}.

The group comprises the identity element `e`, together
with `n`-1 rotations
{`R`_{1}, `R`_{2}
… `R`_{n-1}}, and `n`
reflections {`M`_{1}, `M`_{2}
… `M`_{n}}. The identity and the
rotations form a cyclic sub-group of
order `n`. There are `n` sub-groups of order 2
each formed by the identity and a single reflection. Additional
sub-groups (including more of order 2 and `n` may be
possible depending on the factors of `n`.

Special Cases:
`D`_{2} = `C`_{2} ;
`D`_{4} = `C`_{2} × `C`_{2} .