Tables for
Volume G
Definition and exchange of crystallographic data
Edited by S. R. Hall and B. McMahon

International Tables for Crystallography (2006). Vol. G, ch. 3.8, p. 206

Section 3.8.1. Introduction

I. D. Browna*

aBrockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada L8S 4M1
Correspondence e-mail:

3.8.1. Introduction

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Symmetry lies at the heart of crystallography. Volume A of International Tables for Crystallography (2005[link]) (IT A) is among the most widely consulted crystallographic texts, since it defines the concepts underlying the theory of three-dimensional crystal symmetry and gives detailed descriptions of the 230 different space groups. These descriptions are essential for anyone studying crystals, since no structure report is complete if the space group is not given.

For this reason, the original core CIF dictionary included a small number of the essential items needed to describe the symmetry of a crystal structure. Among these were three different forms of the space-group name (symbol) and a listing of the symmetry operations in algebraic form. This group of items has proved sufficient for the purpose of archiving crystal structures, but it does not readily lend itself to further extension.

Symmetry concepts have precise definitions, which makes them particularly amenable to manipulation by computer. It is therefore natural to consider the ways in which the concepts of space-group theory and practice should be represented in CIF. Possible applications for an extended list of symmetry items in CIF include online access to the tables given in International Tables for Crystallography Volume A (properties of space groups), Volume A1 (relationships between space groups) and Volume E (properties of layer and frieze groups), as well as to allow the description of higher-dimensional symmetry in CIFs reporting quasicrystal, magnetic and modulated structures. To be effective, any CIF definitions have to reflect the current state of space-group theory, as well as meeting the needs of future software that will automatically assemble and manipulate information drawn from crystallographic and other databases.


International Tables for Crystallography (2005). Vol. A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers.

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