## Crystalline Symmetries, An Informal Mathematical IntroductionCrystalline Symmetries: an informal mathematical introduction is a guided tour through the maze of mathematical models and classifications that are used today to describe the symmetries of crystals. The mathematical basis of crystallography and the interpretation of The International Tables for X-ray Crystallography are explained in a heuristic and accessible way. In addition to discussing standard crystals, a special feature of this book is the chapter on generalised crystals and the Penrose tile model for the kinds of generalised crystals known as quasicrystals. This fruitful interaction between pure mathematics (symmetry, tilings) and physics should prove invaluable to final year undergraduate/graduate physicists and materials scientists; the reader gets a flavour of the powerful coherence of a group theoretical approach to crystallography. Mathematicians interested in applications of group theory to physical science will also find this book useful. |

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### Contents

Symmetry and point groups | 20 |

Lattices | 39 |

The space groups | 59 |

Copyright | |

5 other sections not shown

### Common terms and phrases

appear assigned atomic axis band Bravais called century Chapter classes classification colors configuration consider construction contains correspond cosets crystal structure crystallography cube diffraction patterns dimensions discussed distance edges elements enumerated equally equation equivalent example explain faces fact Figure finite five fixed four geometry helpful hexagons ideas identical important infinite integer interest International interpretation isometries kinds known lattice planes lattice point layer mathematical means multiplication N-dimensional nonperiodic normal objects orbit origin orthogonal parallel Penrose tiles permutation plane point group poles polygons positions possible problem projected properties reasons reflection regular relation represent rotation rules sectors shapes shown in Figure shows single space groups sphere stabilizer subgroup symmetry group symmetry operations Tables Theorem theory three-dimensional tion transform translation two-dimensional understand unit cell vectors vertices Voronoļ cell x-ray