UNIFIED SYSTEM OF HERMANN-MAUGUIN SYMBOLS FOR GROUPS OF MATERIAL PHYSICS. Vojtech Kopsky, Institute of Physics, Czech Acad. Sci., Na Slovance 2, POB 24, 180 40 Praha 8, Czech Republic

A mathematically justified system of Hermann-Mauguin symbols of the following properties is proposed for groups of material physics:

1. It is based on the same principles as the traditional symbols for space groups.

2. Symbols of linear, frieze, plane, rod, layer, and space groups with discrete, continuous and semicontinuous lattices are included.

3. Each specific group is expressed with reference to a crystallographic basis by a single symbol with space shift in parentheses.

4. All possible settings and cell choices are described for monoclinic and orthorhombic groups.

5. The symbols of reducible space (plane) groups are correlated with symbols of rod and layer (frieze) groups through projections in which subperiodic groups appear as factor groups of reducible space groups.

6. Groups with standard symbols are chosen in each arithmetic class in such a way that they constitute a group under so-called Baer multiplication.

The system constitutes a background for a unified nomenclature of space and subperiodic groups up to three dimensions in which the relationship between reducible space groups and subperiodic groups is extremely transparent. The proposal is submitted to the Commission for Crystallographic Nomenclature. Proposed symbols of frieze, rod and layer groups will be used in Vol. E: "Subperiodic Groups" of the "International Tables for Crystallography". Relationships between groups will be illustrated by tables and diagrams and examples of the use of the system in applications will be demonstrated.