## 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)).

### MSC:

 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

### Keywords:

nonperiodic tilings; quasicrystals; lattices

### Citations:

Zbl 0838.52023; Zbl 0880.00009