2003/04/24 by B. Souvignier · 1 citation
Materials Science · Mathematics · Chemistry · #Quasicrystal Structures and Properties #X-ray Diffraction in Crystallography #Crystallization and Solubility Studies #Group (periodic table) #Mathematics #Classification scheme #Space (punctuation) #Enumeration #Point group #Space group #Crystal (programming language) #Point (geometry) #Harmonic #Combinatorics #Crystallography #Pure mathematics #Geometry #Physics #Computer science #Chemistry #X-ray crystallography #Quantum mechanics #Diffraction
paper · pdf · doi:10.1107/s0108767303004161
openalex publication_date 2003/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
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.