Advances in materials science have given rise to novel materials with unique properties, through the manipulation of structure at the atomic level. Elucidating the shape and form of matter at this scale requires the application of mathematical concepts. This 2006 book presents the geometrical ideas that are being developed and integrated into materials science to provide descriptors and enable visualisation of the atomic arrangements in three-dimensional space. Emphasis is placed on the intuitive understanding of geometrical principles, presented through numerous illustrations. Mathematical complexity is kept to a minimum and only a superficial knowledge of vectors and matrices is required, making this an accessible introduction to the area. With a comprehensive reference list, this book will appeal to those working in crystallography, solid state and materials science.

• Provides an extensive overview of current developments in materials science • Uses over 200 illustrations to develop an intuitive understanding of geometrical principles, with a colour plate section to aid comprehension • The relevant mathematical techniques are introduced, making the topic accessible to readers with only limited knowledge of vectors and matrices

### Contents

1. Introduction; 2. 2D Tilings; 3. 3D Tilings; 4. Circle and sphere packing; 5. Hierarchical structures; 6. Clusters; 7. Helical and spiral structures; 8. 3D Nets; 9. Triply periodic surfaces; 10. Novel atomic configurations in metallics.

### Reviews

Review of the hardback: '… gives a well-organised description of the geometries of these materials at a mathematical level which should not be too frightening to any graduate chemist … it will appeal to those working in crystallography, metallurgy, solid state and materials science.' Chemistry World

Review of the hardback: '… written in a pleasant, easy to read style. The book is a valuable source of reference and information for all mathematicians interested in geometry and its applications to materials sciences. It will certainly contribute to the fruitful and exciting dialogue between materials scientists and mathematicians.' Zentralblatt MATH