AN APPARENTLY PARADOXICAL SITUATION IN SOME CENTROSYMMETRIC SPACE GROUPS. Siddhartha Ray, Department of Solid State Physics, Indian Association for the Cultivation of Science, Jadavpur, Calcutta-700032, India

In some centrosymmetric space groups belonging to the uniaxial systems, there may exist two `polar descriptions' of the same structure depending on the choice of the positive direction of the unique axis and not interrelated by any operation of the space group. Referred to hexagonal or tetragonal axes, the corresponding sets of atomic coordinates are related by the transformation (0 1 0/1 0 0/0 0 -1) and may be assigned the arbitrary nomenclature `c-up and c-down descriptions'. This apparently paradoxical situation would arise in R3, P3, P4/m, P6/m and in any other space group which does not include the above transformation as one of the symmetry operations,--a fact to be considered while looking for isostructurality of two crystals with one of such space groups.