INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY VOL.A2 N-DIMENSIONAL CRYSTALLOGRAPHY. T. Janssen, University of Nijmegen, Nijmegen, The Netherlands

This volume will consist of a computer programme and an accompanying printed volume with a manual and a treatment of the theory of symmetry in arbitrary dimension. This implies that it gives the information on two- and three-dimensional point groups and space groups as well. For more than three dimensions these groups are used already by crystallographers dealing with incommensurate phases and quasicrystals.

The quickly increasing number of space groups when one goes to higher dimensions makes it inconvenient to present the information as a printed volume. The idea behind the programme is that one generates the information from data in a data base only for those cases that present themselves in practice. From the data base are calculated the space groups, the symmetry elements, the Wyckoff positions, the general and special extinction rules, in short all that can be found in the existing tables for 2 and 3 dimensions, with the advantage that it will be easy to change origin and setting in an arbitrary way.

The interaction between user and computer goes via menus, with which one can make a selection, and via a list of instructions, written in a special language, if one wants to go beyond the preset selections. The results are also presented in graphical form, for example as presentations in 3 dimensions of symmetry elements and crystal structures that are described by means of the symmetry groups of arbitrary dimension. For the usual two- and three-dimensional structures this is no problem. For systems with higher-dimensional symmetry groups, the physical structure is the restriction to physical space of a higher-dimensional lattice-periodic structure. This can be viewed by selecting a volume in three-dimensional space and plotting the intersection of the higher-dimensional structure with this volume.

The programme will be constructed to be used on a variety of platforms, such as IBM-type PC's, MacIntosh and Unix work stations.

The theory of higher-dimensional crystallography and the nomenclature, as far as it will have crystallized out, will be given in a printed volume.