## Crystallographic and metacrystallographic groups |

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### Contents

Sets mappings classifications and algebraic structures | 3 |

A selection of definitions and theorems concerning groups | 10 |

Leading to spacetime | 87 |

Copyright | |

22 other sections not shown

### Common terms and phrases

arithmetic classes atom automorphism basis Bravais class Bravais group Bravais space group called Chapter classes of space colour groups column conjugate subgroups consists constitute coordinate system crystallographic groups defined definition denoted direct product DR(F equation equivalence classes Euclidean group Euclidean point space example follows geometric classes group G group of isometries groups of rotations H-M symbol homomorphism identical improper rotations integers invariance group inversion isometries isomorphic lattice group left cosets line groups linear listed magnetic groups magnetic lattice groups magnetic point lattices magnetic space groups mapped matrix group matrix representation non-symmorphic space group normal subgroup notation obtained one-dimensional orthogonal pair permutation representation point group point lattice proper affine class proper rotations quotient groups real numbers semidirect product simple crystal specified spin arrangement spin groups strictly equivalent subdirect product subgroup of G subgroup of index superspace groups symmetry group symmorphic space group Table Theorem translation unit element VE(n