Infinite dihedral group

The infinite dihedral group, usually denoted as \( D_{\infty} \) or sometimes \( D_{\infty}^* \), is a mathematical structure in group theory that extends the concept of the dihedral groups. While the finite dihedral group \( D_n \) represents the symmetries of a regular polygon with \( n \) sides (including rotations and reflections), the infinite dihedral group captures symmetries of an infinite linear arrangement.