An Introduction to Mathematical Crystallography |
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3-fold symmetry angles Appendix arrays bearing in mind body-centred C³M³ Chapter characterised coincides combined configurations construct coordinates corresponding crystal crystallographic point groups cube cyclic groups describes a rotation dihedral group displayed in Fig end-centred orthorhombic equation equivalent exhibits face-centred cubic factor group follows glide groups which qualify Hence hexagonal cell horizontal 2-fold axis horizontal mirror hp+kq+lr hx+ky+lz identical atoms implies inversion centre isomorphous J(hkl lattice point lattice translation operator lattice vector mathematical matrix mirror plane monoclinic monoclinic cell motif structure motif unit n-fold obtain orthorhombic orthorhombic cell parallel point symmetries point-group symmetry possible primitive cell properties Prove pure axial symmetries reciprocal lattice reflection replacing respectively rhombohedral rhombus rigid-body translation roto-reflection screw axes Show Similarly space groups space lattice stacking pattern symbol symbolised symmetry elements tetragonal tetrahedral group transformation two-dimensional unit cell vertical mirror vertical symmetry axis