A dihedral group is a mathematical structure that represents the symmetries of a regular polygon, including both rotations and reflections. The dihedral group of order n, denoted as D_n, consists of n rotations and n reflections, capturing all the ways to map the polygon onto itself while preserving its structure. This concept is crucial for understanding group theory and has important applications in combinatorics and geometry, particularly when applying Burnside's lemma.
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