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**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)).

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)).

Reviewer: M.Baake (Tübingen)

### 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 |

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\textit{M. Senechal}, Quasicrystals and geometry. Cambridge: Cambridge Univ. Press (1995; Zbl 0828.52007)

### Online Encyclopedia of Integer Sequences:

Irregular array read by rows: T(n,k) = number of r_{n,k}-cores associated with A233332(n,k), for n>=2, 1<=k<=floor(n/2), explained below.Irregular array read by rows: T(n,k) = number of r_{n,k}-cores associated with A233332(n,k), reduced for symmetry, for n>=2, 1<=k<=floor(n/2), explained below.

Irregular array read by rows: A(n,k) = number of first coronas of a fixed rhombus r_{n,k} with characteristics of n-fold rotational symmetry in the Euclidean plane, n>=2, 1<=k<=floor(n/2), as explained below.

Irregular array read by rows: A(n,k) = number of first coronas of a fixed rhombus r_{n,k} with characteristics of n-fold rotational symmetry in the Euclidean plane, n>=2, 1<=k<=floor(n/2), reduced for symmetry, as explained below.

Coordination sequence for planar net 3.3.3.3.6 (also called the fsz net).