Experimental Mathematics

Counting crystallographic groups in low dimensions

Wilhelm Plesken and Tilman Schulz

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.

Article information

Source
Experiment. Math. Volume 9, Issue 3 (2000), 407-411.

Dates
First available: 18 February 2003

Permanent link to this document
http://projecteuclid.org/euclid.em/1045604675

Mathematical Reviews number (MathSciNet)
MR1795312

Zentralblatt MATH identifier
0965.20031

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

Citation

Plesken, Wilhelm; Schulz, Tilman. Counting crystallographic groups in low dimensions. Experimental Mathematics 9 (2000), no. 3, 407--411. http://projecteuclid.org/euclid.em/1045604675.


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