What a lovely shape

New geometries for new materials 

Eric Lord, Alam Mackay and S Ranganathan 

Cambridge, UK: Cambridge University Press |2006 | 238pp | ?70.00 (HB) | ISBN 0521861047 

Reviewed by Tim Salkield

Materials science has exploded in recent years and with this explosion has come the need for mathematical descriptions of the geometry involved. Maths previously considered as theoretical has now been harnessed to describe the 3D structures in natural and synthetic materials such as zeolites, silicates, aluminosilicates, fullerenes, quasicrystalline alloys, and liquid crystals. 

This book, which stems from a project sponsored by the Defence, research and development organisation, ministry of defence, government of India, 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. The principles of symmetry and topology pervade the pages, while the authors briefly introduce the mathematics of minimal surfaces. There are chapters on 2D and 3D tilings, circle and sphere packing, hierarchical structures, clusters, helical and spiral structures, 3D nets, triply periodic surfaces and novel atomic configurations in metallics. 

The book is well illustrated, although I think it should have been published in colour throughout to make it even easier for the reader to visualise the many 3D shapes. It will appeal to those working in crystallography, metallurgy, solid state and materials science. 

At the end of the book, details are given of the software that is available to handle such 3D geometrical shapes, such as Mathematica, Surface Evolver, and Povray.