Dihedral Group

A dihedral group describes all the symmetries of a regular polygon, including rotations and reflections. For example, the symmetries of a square, which can be rotated by 90°, 180°, 270°, or flipped along lines of symmetry, form a dihedral group. It captures how the shape can be transformed without changing its appearance. These groups are fundamental in understanding symmetry in mathematics and related fields, demonstrating how an object can be manipulated yet remain unchanged in shape and structure.