IUCr 1993 Triennial Report - Volume F. Multidimensional Crystallography

No direct progress has been made with planning a volume on N-dimensional crystallography (N > 3). An enthusiastic editor is lacking, and the great number of space groups is a problem. However, the Working Group set up in 1990 by the Commission on Crystallographic Nomenclature has in effect functioned also as a sub-committee of the Commission on International Tables; two editors are members of the Working Group, and the other Editors have been consulted as occasion required. It has not proved possible to reach any unanimous recommendations, but discussion within the group and with others interested in the problem has resulted in the clarification of many problems and the publication of new or revised versions of the systems favoured by some members of the group.

The Commission on International Tables has a problem of size on its hands. For the description of the symmetry of the complex electron density when dispersion is appreciable and related problems (the Patterson synthesis; certain magnetic properties) `coloured' (Shubnikov) space groups are required; there are 1651 dichromatic groups. The only reasonably complete treatment of the dichromatic groups is in Russian (V. A. Koptsik, Shubnikov Groups. Moscow University Press, 1966) and is out of print. It is much less detailed than Volume A of International Tables; the entry for each space group contains little more than the equivalent of the diagrams of Volume A. Such colour groups in three dimensions are subperiodic groups of the 4895 space groups in four dimensions [H. Heesch (1930). Z. Kristallogr. 73, 325-345]. It takes about 800 pages to treat the 230 three-dimensional space groups in Volume A, an average of 3.5 pages per group. Pro rata, it would require a volume of 5800 pages to treat the colour groups in the same detail, and one of 17000 pages for the four-dimensional space groups. `Volumes' of such a size are not impossible - they would amount to about the complete Oxford English Dictionary and the Encyclopaedia Britannica, respectively - but are they practicable? The material could be produced largely as direct computer output and distributed as a volume of about the current size plus one or two compact disks. Readers for compact disks are not widely available as yet, but may be expected to become common within the next few years. Alternatively, computer programs for generating the space-group entries could accompany the single printed volume.

13 April 1993                            A. J. C. WILSON, Chairman

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