A Classification of the Possible Symmetry Groups of Liquid Crystals

A classification of all the possible groups of rigid transformations, namely rotations, reffections, translations, screw axes and glide planes, is presented. These groups are the subgroups of the centrosymmetric Euclidean group. They may be used to describe the symmetry of crystals, liquids, amorphous solids, powders, and liquid crystals. They may also be used to describe the symmetry of systems of lower dimensionality, as surfaces, thin layers, etc.