2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110001The paper presents mathematical models of quasicrystals with particular attention given to cut-and-project sets. We summarize the properties of higher-dimensional quasicrystal models and then focus on the one-dimensional ones. For the description of their properties we use the methods of combinatorics on words.19 pages, 3 postscript figures, contribution to the Proceedings of NATO School "Physics and Computer Science", Cargese 2005Mathematical PhysicsCombinatorics52C23 (primary) 68R15 (secondary)text