The [symmetries](Algebra%20(index).md#Symmetry) for rotations of [regular polygons](Geometry%20(index).md#Regular%20polygons) where their center is at an [origin](Geometry%20(index).md#origin) are called _dihedral groups._ The dihedral group for a [regular polygons n-sided](Geometry%20(index).md#Regular%20polygons) polygon contains $2n$ elements and thus this group is denoted as $\mbox{D}_{2n}.$ #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Groups #MathematicalFoundations/Geometry