THE FUNDAMENTAL REGIONS OF THE POINT SYMMETRY GROUPS AS THE BASIS OF THE CLASSIFICATION OF THE STRUCTURAL STATES OF SUBSTANCE. N. V. Fyodorova, V. M. Talanov, State Technical University, Novocherkassk, 346400, Russia

We suggest the classification of types of the structural states of substance on the basis of the analysis of the point symmetry groups fundamental regions. The following types of the structural states are examine: isosymmetric, enantiomorphous, anti-isostructural, the states of the local increase of symmetry (extraordinary, exceptional), irrational (quasicrystalline) states.

The own isosymmetric states are possible in the 18 point groups (4-3m, 432, m3-, 23, 6/mmm, 6-2m, 6mm, 622, 4/mmm, 4-2m, 4mm, 422, 3-m, 3m, 32, mmm, mm2, 222), in which the fundamental regions are limited by the structural elements of the same types. In the six of them (432, 23, 622, 422, 32, 222), exactly in the turning groups having more then one symmetry axis, there are geometrically and crystallographically enantiomorphous varieties of structural states. The turning groups 2, 3, 4 and 6 occupy the special place, because in this groups the geometrically enantiomorphous states are possible not in the all classes of objects. The own anti-isostructural states are possible in 11 groups (4-3m, 432, 23, 6-2m, 622, 4-2m, 422, 3-m, 3m, 32, 222).

The directions of the local increase of symmetry are subdivided on the two types: extraordinary and exceptional. the first type take place in the 26 point groups (exept m3-m, 6/m, 4/m, 2/m, 1-, 1), in the 6 from which (6/mmm, 6mm, 622, 4/mmm, 4mm, 422) there are irrational extraordinary directions; the second type are observed in the 11 point groups (m3-,23, 4/mmm, 4-2m, 422, 4/m, 4-, 3-m, 32, 3-, 2/m), moreover in all these groups there are irrational exceptional directions.