Quasicrystals and geometry. (English) Zbl 0828.52007

Cambridge: Cambridge Univ. Press. xv, 286 p. (1995).
This book provides an elementary mathematical introduction to nonperiodic tilings and quasicrystals. The adequately chosen selection of topics contains: historic remarks, lattices and quasicrystals, diffraction, order and tilings, classification results, and many illustrative examples. Most parts of the book can already be understood at first-year level, but the reader should be aware of a number of errors not all of which are obvious (the author of the book runs a list with corrections and new developments, accessible via anonymous \(ftp)\).
For further (and complementary) material, the interested reader could consult “Quasicrystals – A Primer” by C. Janot, Clarendon Press, Oxford, 2nd ed. (1994; Zbl 0838.52023) or “Beyond Quasicrystals” (eds. F. Axel and D. Gratias, Springer, Berlin (1995; Zbl 0880.00009)).


52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
82D25 Statistical mechanics of crystals
52-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
20H15 Other geometric groups, including crystallographic groups