The Bilbao Crystallographic Server, URL http://www.cryst.ehu.es, is a web site with crystallographic databases and programs.

The server is built on a core of databases and contains different shells. The set of databases includes data from International Tables for Crystallography, Vol. A: Space-group symmetry (hereafter referred to as IT A), and the data on maximal subgroups of space groups as listed in International Tables for Crystallography, Vol. A1: Symmetry relations between space groups (hereafter referred to as IT A1). There is an access to the crystallographic data for the subperiodic layer and rod groups (International Tables for Crystallography, Vol. E: Subperiodic groups and their maximal subgroups).

The communication with the databases is provided by simple retrieval tools. They allow the access to the information on space groups or subperiodic groups in different types of formats: HTML, text ASCII or XML. In this way the retrieval tools serve not only for obtaining specific information but can also be used as input data for other programs.

The aim of the lecture is to introduce the main symmetry databases of the Bilbao Crystallographic Server and the corresponding access tools. At the same time, the lecture sums up some basic results on important aspects of crystallographic space groups.

The main points of the lecture can be summarized as follows:

1. Space-group symmetry databases (International Tables for Crystallography, Volume A: Space-group symmetry):
   • symmetry operations: matrix-column presentation; geometric interpretation.
   • generation of space groups; generators and general positions, Wyckoff positions.
   • special Wyckoff positions, site symmetry
2. Coordinate transformations: origin shift and change of the bases; conventional and non-conventional descriptions of space groups; ITA-settings.
3. Crystal-structure descriptions I. Structure tools on BCS for crystal-structure descriptions:
   • Basis transformations and crystal-structure descriptions (the program TRANSTRU).
   • Descriptions of crystal structures with respect to different ITA settings of the space groups (the program SETSTRU).
   • Transformation of the unit cell parameters under change of the basis (the program CELLTRAN).
4. Crystallographic data for subperiodic groups (International Tables for Crystallography, Volume E: Subperiodic groups): rod and layer groups.

Supplementary Material