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