Journal
ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES
Volume 59, Issue -, Pages 210-220Publisher
INT UNION CRYSTALLOGRAPHY
DOI: 10.1107/S0108767303004161
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This paper gives classification results for crystallographic groups in dimensions up to 6 which refine earlier enumeration results. Based on the classification data, the asymptotic growth of the number of space-group types is discussed. The classification scheme for crystallographic groups is revisited and a new classification level in between that of geometric and arithmetic crystal classes is introduced and denoted as harmonic crystal classes. Enantiomorphic pairs are determined on all classification levels from space-group types to crystal families and the enantiomorphic pairs of fixed-point-free space groups are given. A general algorithm to compute enantiomorphic pairs is described.
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