This book reports on the latest progress in the new and active field of quasicrystals. A discussion of the characteristic physical properties of quasicrystals will serve researchers as a starting point for further studies.

Inhalt
I Introduction.- to Quasicrystals.- II Symmetry and Generalized Crystallography.- Chains, Flowers, Rings and Peanuts: Graphical Geodesic Lines and Their Application to Penrose Tiling.- The Ehrenfest Process, a Rotational Representation of Spin Operators and Explicit Forms of Rotation Operators.- Generalized Crystallography in Two and Three Dimensions.- III Atomic Structures.- Progress on the Atomic Structure of Quasicrystals.- From Crystal Approximants to Quasicrystals.- Ideal Structures of the Icosahedral Al-Mn and Al-Cu-Li Quasicrystals.- High-Resolution Electron Microscopy and Atomic Arrangement of an Al-Li-Cu Quasicrystal.- IV Quasiperiodic Lattices and Random Tiling.- Icosahedral and Decagonal Quasicrystals in Al-Ni-M and Al-Cu-M (M=Transition Metal) Systems.- Growing Perfect Quasicrystals.- The Alternation Condition and 2D Quasicrystals.- Random Tiling Model of Quasicrystalline Order.- Phason Freezing.- Elastic Instability Induced by Phasons in Icosahedral Quasicrystals.- V Electronic Structure.- Electronic States in a Quasicrystal.- Scaling of Structures, Spectra and Wave Functions.- Multifractal Method for Spectra and Wave Functions of Quasiperiodic Systems.- Localization in One-Dimensional Quasiperiodic Systems.- Quasiperiodic Systems with Long-Range Hierarchical Interactions.- Conductance of a Penrose Lattice.- Electronic Structure in Three-Dimensional Quasicrystals.- VI Spin Statistics.- Monte Carlo Study of Spin Statistics in Two- and Three-Dimensional Quasicrystals.- Index of Contributors.