Point Symmetry

Symmetry may seem like a self-evident property of an object – you know it when you see it – but for the study of crystallography a rigorous definition is required, so here goes: Symmetry is that property possessed by an object when some operation (translation, rotation, reflection, and/or inversion) leaves it indistinguishable from its original position. In other words, symmetry is a demonstration of the invariance of the object to the operation. Topics such as electronic bands, phonon dispersion, vibrational spectroscopy (e.g., Raman and IR), and the properties of crystalline materials generally require a good understanding of crystal symmetry.