N-dimensional Crystallography |
Contents
SYMMETRY IN THE PLANE | 1 |
GROUPS OF AFFINE TRANSFORMATIONS | 18 |
SPACE GROUPS | 26 |
Copyright | |
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Common terms and phrases
abelian action of H additional symmetry affine transformation arithmetic crystal classes axis basis vector black and white Bravais types classes of space cocycle cohomology colour symmetry group conjugacy classes coordinate corresponding coset crystal families crystallographic defined Definition denote determined dimension e₁ element equations equivalence classes equivalence relation exact sequence example Fedorov finite subgroups G₁ geometric crystal classes graphs of class group G H₁ hemihedral hence Hermann-Mauguin notation holohedral homomorphism i-th implies invariant isometries isomorphism classes L₁ L₂ lattice Lemma minimum length modulo n-dimensional orthogonal space groups pair permutation plane groups point group primitive Proposition quotient quotient group reduced basis reflection rotation scalar products Schönflies shift vector shortest non-zero vectors SO(n space groups spans subspace T₁ T₂ tetragonal Theorem Let u₁ V₁ vectors length vertex vertices white groups white lattice α α θε