### Counting crystallographic groups in low dimensions

Wilhelm Plesken and Tilman Schulz
Source: Experiment. Math. Volume 9, Issue 3 (2000), 407-411.

#### Abstract

We present the results of our computations concerning the space groups of dimension 5 and 6. We find 222 018 and 28 927 922 isomorphism types of these groups, respectively. Some overall statistics on the number of $\funnyQ$-classes and $\funnyZ$-classes in dimensions up to six are provided. The computations were done with the package CARAT, which can parametrize, construct and identify all crystallographic groups up to dimension 6.

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Primary Subjects: 20H15
Full-text: Open access