View source for Dihedral group

{{TEX|done}}
''dihedron group''

A finite group isomorphic to the rotation group of a dihedron, i.e. of a regular doubled [[pyramid]]. If the base of the pyramid is an $n$-gon, the corresponding dihedron group is of order $2n$ and is generated by two rotations $\phi$ and $\psi$ of orders $n$ and $2$ respectively, with the defining relation $\phi\psi\phi\psi=1$.  An alternative description is the group of rotations and reflections of a regular $n$-gon, with $\phi$ as a rotation of order $n$ and $\psi$ as a reflection.  In a finite group, two different elements of order 2 generate a dihedral group.

The notation for the group varies: some author write $D_n$ and others $D_{2n}$ for the group of order $2n$.  A dihedral group is sometimes understood to denote the dihedral group of order 8 only. 

See also: [[Quasi-dihedral group]]

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  G.G. Hall,   "Applied group theory" , Longman  (1967)</TD></TR></table>

[[Category:Group theory and generalizations]]