Nomenclature and symbolism of space symmetry groups

Abstract

The developed symbolism makes it possible to solve the problem in the same way and simply in the most general case: given (using a model, drawing or other way) a regular system of points or a combination of several regular systems of points forming a crystal lattice; it is required to find the space symmetry group of this set. We will not present a systematic approach to solving this problem here; we will only point out that the matter comes down to writing the group symbol. To avoid possible errors in choosing orientation and correctly selecting the generating element of symmetry among the set of parallel elements of symmetry of a given direction, a simple “determinant” of space groups has been compiled. Using this determinant, it is possible to determine a group, even if the found group symbol does not correspond to the accepted one for this group. The compilation of such a determinant and a systematic presentation of the progress in solving the problem posed above is the work of the author that has already been completed. The second significant consequence of the proposed symbolism is the ability to carry out a new simple and systematic derivation of 230 space groups.