An Introduction to Mathematical Crystallography |
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angles Appendix bearing in mind Bravais space groups Brillouin zone C³M Chapter characterised coincides configurations construct coordinates corresponding crystal crystallographic point groups cube cyclic groups describes a rotation dihedral group displayed in Fig equation equivalent exhibits face-centred cubic factor group follows geometrical glide groups which qualify Hence horizontal 2-fold axis horizontal mirror hx+ky+lz identical atoms implies inversion centre lattice point lattice translation operator mathematical matrix mirror plane monoclinic monoclinic cell motif structure motif unit non-primitive cells orthorhombic parallel perpendicular point symmetries point-group symmetry possible primitive cell primitive cubic lattice primitive hexagonal primitive rhombohedral cell properties Prove pure axial symmetries reciprocal lattice vector referred reflection replacing respectively rigid-body translation rotational symmetry roto-reflection screw axes setting being designated Show space groups space lattice stacking pattern symbol symmetry axis symmetry elements tetragonal tetragonal cell theorem transformation unit cell vertical mirror wave zone