Tables for
Volume A1
Symmetry relations between space groups
Edited by Hans Wondratschek and Ulrich Müller

International Tables for Crystallography (2011). Vol. A1, ch. 1.7, p. 57

Section 1.7.1. Introduction

Mois I. Aroyo,a* J. Manuel Perez-Mato,a Cesar Capillasa and Hans Wondratschekb

aDepartamento de Física de la Materia Condensada, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, E-48080 Bilbao, Spain, and bInstitut für Kristallographie, Universität, D-76128 Karlsruhe, Germany
Correspondence e-mail:

1.7.1. Introduction

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The Bilbao Crystallographic Server, , is a web site of crystallographic databases and programs. It can be used free of charge from any computer with a web browser via the Internet.

The server is built on a core of databases and contains different shells. The set of databases includes data from the 5th edition of International Tables for Crystallography Volume A, Space-Group Symmetry (2005[link]) (hereafter referred to as IT A) and the data for maximal subgroups of space groups as listed in Part 2 of this volume (hereafter referred to as IT A1). Access is also provided to the crystallographic data for the subperiodic layer and rod groups [International Tables for Crystallography, Volume E, Subperiodic Groups (2002[link])] and their maximal subgroups. A database on incommensurate structures incorporating modu­lated structures and composites, and a k-vector database with Brillouin-zone figures and classification tables of the wave­vectors for space groups are also available.

Communication with the databases is achieved by simple retrieval tools. They allow access to the information on space groups or subperiodic groups in different types of formats: HTML, text ASCII or XML. The next shell includes programs related to group–subgroup relations of space groups. These programs use the retrieval tools for accessing the necessary space-group information and apply group-theoretical algo­rithms in order to obtain specific results which are not available in the data­bases. There follows a shell with programs on representation theory of space groups and point groups and further useful sym­metry information. Parallel to the crystallographic software, a shell with programs facilitating the study of specific problems related to solid-state physics, structural chemistry and crystallography has also been developed.

The server has been operating since 1998, and new programs and applications are being added (Kroumova, Perez-Mato, Aroyo et al., 1998[link]; Aroyo, Perez-Mato et al., 2006[link]; Aroyo, Kirov et al., 2006[link]). The aim of the present chapter is to report on the different databases and programs of the server related to the subject of this volume. Parts of these databases and programs have already been described in Aroyo, Perez-Mato et al. (2006[link]), and here we follow closely that presentation. The chapter is completed by the description of the new developments up to 2007.

The relevant databases and retrieval tools that access the stored symmetry information are presented in Section 1.7.2[link]. The discussion of the accompanying applications is focused on the crystallographic computing programs related to group–subgroup and group–supergroup relations between space groups (Section 1.7.3[link]). The program for the analysis of the relations of the Wyckoff positions for a group–subgroup pair of space groups is presented in Section 1.7.4[link]. The underlying group-theoretical background of the programs is briefly explained and details of the necessary input data and the output are given. The use of the programs is demonstrated by illustrative examples.


Aroyo, M. I., Kirov, A., Capillas, C., Perez-Mato, J. M. & Wondratschek, H. (2006). Bilbao Crystallographic Server. II. Representations of crys­t­allographic point groups and space groups. Acta Cryst. A62, 115–128.
Aroyo, M. I., Perez-Mato, J. M., Capillas, C., Kroumova, E., Ivantchev, S., Madariaga, G., Kirov, A. & Wondratschek, H. (2006). Bilbao Crystallographic Server: I. Databases and crystallographic computing programs. Z. Kristallogr. 221, 15–27.
International Tables for Crystallography (2005). Vol. A, Space-Group Symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers.
International Tables for Crystallography (2002). Vol. E, Subperiodic Groups, edited by V. Kopský & D. B. Litvin. Dordrecht: Kluwer Academic Publishers.
Kroumova, E., Perez-Mato, J. M., Aroyo, M. I., Ivantchev, S., Madariaga, G. & Wondratschek, H. (1998). The Bilbao Crystallographic Server: a web site with crystallographic tools using the International Tables for Crystallography. Abstracts of the 18th European Crystallographic Meeting, Prague, Czech Republic.

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