Converting one-line symbols to two-line symbols of (3+1)-dimensional superspace groups

There are two kinds of superspace-group symbols [see Section 3.1 and Table 1 of A. Yamamoto's paper, Acta Cryst. (1996) A52 509-560], i.e. one-line symbols and two-line symbols. For historical reason, the program SPGR4D [J. Appl. Cryst. (1997). 30, 73-78] in DIMS can only recognize two-line symbols. The program symbol1to2 is wriitten for converting one-line symbols to two-line symbols of (3+1)-dimensional superspace groups. It can distinguish two-line symbols from one-line symbols. When the input symbol belongs to two-line symbols, symbol1to2 will invoke SPGR4D and pass on directly the input symbol to it. SPGR4D will then derive and output the corresponding symmetry operations. On the other hand, if the input symbol belongs to one-line symbols, symbol1to2 will derive the corresponding two-line symbol and then pass on the result to SPGR4D to get the symmetry operations.

775 non-equivalent one-line symbols of (3+1)-dimensional superspace groups listed in the International Tables for Crystallography [Janssen, T., Janner, A., Loouenga-Vos, A., de Wolff, P.M. (2006) International Tables for Crystallography Vol. C, Chapter 9.8, Table, pp. 922-934] were input to symbol1to2 and the resultant symmetry operations from SPGR4D were compared with those listed by Ivan P. Orlov on the Web at There are 229 among the total 775 superspace groups, of which symmetry operations derived by SPGR4D are different from that listed by Orlov. This is owing to the shift of unit-cell origin and/or the direction choice of the 4th axis. Details are available here.

         Li, X.M., Li, F.H. & Fan, H.F. (2009). A revised version of the program VEC. Chinese Physics B 18, 2459-2463. PDF file