Crystal symmetry Hermann-Mauguin notations

These simple examples serve to show that instinctive ideas about symmetry are not going to get us very far. We must put symmetry classification on a much firmer footing if it is to be useful. In order to do this we need to define only five types of elements of symmetry - and one of these is almost trivial. In discussing these we refer only to the free molecule, realized in the gas phase at low pressure, and not, for example, to crystals which have additional elements of symmetry relating the positions of different molecules within the unit cell. We shall use, therefore, the Schdnflies notation rather than the Hermann-Mauguin notation favoured in crystallography. 

The complete designation of the symmetry of a crystal requires the correct assignment of axes and identification of (he symmetry elements. There are a total of 32 different combinations of symmetry elements. Each of these has a unique Hermann-Mauguin notation or point group and is called a crystal class. The 32 crystal classes can be divided into six crystal systems. We will (ry to give you an appreciation of point groups and crystal classes, but our main emphasis will be on the more general crystal systems. 

Understanding the symmetries features of crystals by their resumed notations (Schoenflies and intemational/Hermann-Mauguin) as well as by their specific habitus influencing their morphology (external shape) as paralleling the irmer planes and symmetries at the unit cell level ... 

Note. The Hermann-Mauguin space group notation for any particular crystal comprises two parts. The first part identifies the Bravais lattice type into which the crystal belongs and the second part identifies the total symmetry of the array of atoms in the crystal and therefore also the crystal system. In the second part that identifies the symmetry, only those symmetry elements are included in the symbol that are necessary to describe the space group uniquely. The remainders are being omitted since they follow, as a necessary consequence. 

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