Hermann-Mauguin Symbols

The symbols used in this text are based on notations developed by C. H. Hermann and C. V. Mauguin in the early 1900s. They have been employed by most crystallographers since about 1930. Numbers refer to rotation axes of symmetry; a bar over a number indicates a rotoinversion axis. Mirrors, designated by m, are perpendicular to an axis if they appear as a denominator (for example, ), and parallel to an axis otherwise. When articulating the symbols, they're pronounced even as if they were typographical characters.

For hexagonal point groups, the primary symbol describes the only optic axis . The second, if present, describes three secondary rotation axes oriented at to every other and perpendicular to the optic axis , or three mirror planes oriented at to every other and parallel to the principal axis. The third symbol, if present, represents mirror planes or 2-fold axes oriented between the secondary axes.

For tetragonal point groups, the primary symbol represents the optic axis . The second, if present, represents two secondary axes perpendicular to every other and to the optic axis , or two mirror planes oriented at to every other and parallel to the principal axis. Only three orthorhombic point groups are possible. Point group 222 has three mutually perpendicular 2-fold Point group has three perpendicular 2-fold axes with mirror planes perpendicular to each. mirror, or a 2-fold axis with a mirror perpendicular thereto . Similarly, for triclinic crystals, the sole possible point groups are 1 and 1.