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Concept
Dihedral group
Summary
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry.
The notation for the dihedral group differs in geometry and abstract algebra. In geometry, D''n'' or Dih''n'' refers to the symmetries of the n-gon, a group of order 2n. In abstract algebra, D2''n'' refers to this same dihedral group. This article uses the geometric convention, D''n''.
Definition
Elements
A regular polygon with n sides has 2n different symmetries: n rotational symmetries and n reflection symmetries. Usually, we take n \ge 3 here. The associated rotations and reflections make up the dihedral group \mathrm{D}_n. If n is odd, each axis of symmetry connects
Official source
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