## Experimental Mathematics

### Counting crystallographic groups in low dimensions

#### 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 in Project Euclid: 18 February 2003

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

Mathematical Reviews number (MathSciNet)
MR1795312

Zentralblatt MATH identifier
0965.20031

#### Citation

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