Mirror Symmetry: The Mother of All Crystal Symmetries (2024)

This graduate-level textbook deals with different aspects of plane mirrors and mirror-related symmetries. It provides us with some new ways of understanding symmetries in crystals and the mirror combination schemes. The inclusion of topics such as the Wigner-Seitz unit cell, reciprocal lattice, Brillouin zones, diffraction of crystals, etc., based on the mirror combination scheme, are extremely helpful in understanding many other concepts in crystallography. A mirror is the only fundamental symmetry in crystals, and all other permissible symmetries in crystalline solids can be derived from suitable combinations of mirrors, called derived symmetries. A rudimentary knowledge of symmetry in crystallography is essential to students, researchers, and professionals in many subjects in science and technology: physics, chemistry, mathematics, molecular biology, geology, metallurgy, and particularly materials science and mineralogy.