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• W2002457178 abstract "CONTENTSIntroductionChapter I. Group approach §1. Two-dimensional quasicrystallographic groups1.1. Finite generation of two-dimensional quasicrystallographic groups1.2. Examples of two-dimensional quasicrystallographic groups with infinite point group. Classification of admissible rotation angles1.3. Classification of two-dimensional quasicrystallographic groups with finite point group §2. Three-dimensional and multidimensional quasicrystallographic groups with finite point group2.1. The abstract construction of quasicrystallographic groups with finite point group2.2. Classification of admissible representations in certain special cases §3. Connection with other approaches and definitions3.1. Connection between quasiperiodic tilings and quasicrystallographic groups3.2. Connection with projections of multidimensional crystals3.3. Connection with the Mermin-Rokhsar-Wright phase multipliers3.4. Connection with the generalized Mermin-Rokhsar-Wright phase multipliers. The case of an infinite point group §4. Quasicrystallographic groups with infinite point group4.1. Complete reducibility and pseudo-orthogonality of the action of the point group on a quasilattice4.2. Classification of admissible rotation angles in the case of a quadratic quasilattice4.3. Some examples4.4. Questions connected with finite generationChapter II. The geometry of local rules §1. Definitions and notation §2. Quasiperiodicity and local rules2.1. Projection method and quasiperiodicity2.2. An example of quasiperiodic local rules2.3. The section method2.4. The construction of local rules §3. The geometry of the forbidden set3.1. The topology of complements of 2-planes §4. Multidimensional case §5. An example of local rulesAcknowledgementsAppendices1. Tilings with -symmetry2. Generalization to the case References" @default.
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• W2002457178 date "1993-02-28" @default.
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• W2002457178 title "The geometry of quasicrystals" @default.
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• W2002457178 doi "https://doi.org/10.1070/rm1993v048n01abeh000985" @default.
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