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Dihedral group - Wikipedia

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In mathematics, a dihedral group is the group of symmetries of a regular polygon,[1][2] 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.[3] The notation for the dihedral group differs in geometry and abstract algebra. In geometry, Dn or Dihn refers to the symmetries of the n-gon, a group of order 2n. In abstract algebra, D2n refers to this same dihedral group.[4] This article uses the geometric convention, Dn. The word "dihedral" comes from "di-" and "-hedron". The latter comes from the Greek word hédra, which means "face of a geometrical solid". Overall, it thus refers to the two faces of a polygon. A regular polygon with 𝑛 sides has 2 𝑛 different symmetries: 𝑛 rotational symmetries and 𝑛 reflection symmetries; here, 𝑛 ≥ 3 . The associated rotations and reflections make up the dihedral group D 𝑛 . If 𝑛 is odd, each axis of symmetry con

Dihedral group - Wikipedia Jump to content From Wikipedia, the free encyclopedia Group of symmetries of a regular polygon Algebraic structure → Group theory Group theory Basic notions Subgroup Normal subgroup Group action Quotient group (Semi-) direct product Direct sum Free product Wreath product Group homomorphisms kernel image simple finite infinite continuous multiplicative additive cyclic abelian dihedral nilpotent solvable Glossary of group theory List of group theory topics Finite groups Cyclic group Z n Symmetric group S n Alternating group A n Dihedral group D n Quaternion group Q Cau

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