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 ℚ -classes and ℤ -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.