In mathematics, a dihedral group is the group of symmetries of a regular polygon, including both 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. It is well-known and quite trivial to prove that a group generated by two involutions is a dihedral group.
See also: Dihedral symmetry in three dimensionsRead more about Dihedral Group: Notation, Small Dihedral Groups, The Dihedral Group As Symmetry Group in 2D and Rotation Group in 3D, Equivalent Definitions, Properties, Automorphism Group, Generalizations
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“Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
—Willa Cather (1873–1947)