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Crystallographic Point Groups
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2-fold axes 2-fold rotation A-atom Abelian group Appendix axial mirror planes bearing in mind body-centred Chap colour groupoids colour groups colour space groups colour symmetries configurations construct corresponding crystal model Crystal system Lattice crystallographic point groups crystallographic symmetries cube cyclic group decompositions defined diamond glide dihedral groups displayed in Fig end-centred equivalent atoms exist face-centred cubic follows geometrical glide planes glide reflections hexagonal cell independent integers intersecting lattice plane lattice point lattice vectors m m m macroscopic mathematical microscopic symmetry monoclinic motif pattern non-Bravais non-primitive obtain orthorhombic perpendicular point-group operator point-group symmetry principal symmetry axis providing rhombohedral rhombohedral cell rigid-body translation rotation axis screw axes screw operator secondary 2-fold secondary axes signifies Similarly space lattice symbol symmetry 432 symmetry centre symmetry elements symmetry patterns symmorphic system Lattice type tetragonal theorem theory transformation translation operators triclinic unit cell utilising yielding the colour