This is joint work with Alice C. Niemeyer and Reymond Akpanya
In 1911 Bieberbach solved the 18. of Hilberts 23 problems, by showing that there are only finitely many crystallographic groups of a given dimension. The definition of a crystallographic group of dimension $n$ requires the existence of a fundamental domain, a certain subset of $\R^n$, which there are many of for any given group. However computing any one of them is quite difficult, as crystallographic groups are of infinite order. In this talk, an algorithm is presented that uses Dirichlet cells, a concept closely related to Voronoi domains. The algorithm assumes some knowledge of the crystallographic group, which for all groups of small dimension (up to 6) is already known.