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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[1990] IUCr Triennial Report: Volume F. *Multidimensional Crystallography*

Updated 30th March 1997

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