The CARAT Homepage

CARAT is a computer package which handles enumeration, construction, recognition, and comparison problems for crystallographic groups up to dimension 6. The name CARAT itself is an acronym for Crystallographic AlgoRithms And Tables.

CARAT is a compilation of various programs written in C developed under HP-UX and Linux, and should be portable to most Unices.

In particular CARAT does not come together with an environment, but relies on the ordinary unixes shell and files for input and output. This is one of the points which distiguishes CARAT from most other packages for computer algebra, like GAP . If you would like such a user interface, the current version of GAP comes with an interface to CARAT, which enables one to use the most important functions of CARAT, but not all.

Some of the features of CARAT

CARAT-introduction and Page of low dimensional Bieberbach groups


Below we listes a few papers dealing with CARAT or have been written with the help of it:

As a result, we have the following table for Crystallographic and Bieberbach groups up to dimension 6:

1 2 3 4 5 6
No of Q-classes 2 10 32 227 955 7103
No of Z-classes 2 13 73 710 6079 85308
No of affine classes 2 17 219 4783 222,018 28,927,915
No of Bieberbach groups 1 2 10 74 1060 38746


You can download the newest version of CARAT (version 2.1b1 from 2008-07-19). For installation, please extract the file downloaded and refer to the file

Changes of the new version


If you have any question concerning CARAT (ie. installation etc.), or find a bug in the package, please do not hesitate to contact us:

Lehrstuhl B für Mathematik
Prof. Dr. i.R. W. Plesken
Pontdriesch 10-16
52062 Aachen
Tel: +49 241 80 97079

Lehrstuhl B für Mathematik e-Mail Up