Experimental Mathematics

Computation of Five- and Six-Dimensional Bieberbach Groups

Carlos Cid and Tilman Schulz


This paper deals with the computation and classification of 5- and 6-dimensional torsion-free crystallographic groups, known as Bieberbach groups. We describe the basis of an algorithm that decides torsion-freeness of a crystallographic group as well as the triviality of its centre. The computations were done using the computer package CARAT, which handles enumeration, construction, recognition and comparison problems for crystallographic groups up to dimension 6. The complete list of isomorphism types of Bieberbach groups up to dimension 6 can be found online.

Article information

Experiment. Math., Volume 10, Issue 1 (2001), 109-115.

First available in Project Euclid: 30 August 2001

Permanent link to this document

Mathematical Reviews number (MathSciNet)
MR1 822 856

Zentralblatt MATH identifier

Primary: 20H15: Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]


Cid, Carlos; Schulz, Tilman. Computation of Five- and Six-Dimensional Bieberbach Groups. Experiment. Math. 10 (2001), no. 1, 109--115. https://projecteuclid.org/euclid.em/999188425

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