An algebraic integer q is a PV number (for Pisot-Vijayaraghavan number), if all its algebraic conjugates (except its complex conjugate, if $q$ is complex) are less than one in modulus. A profound theorem by Meyer states essentially, that a substitution tiling can only be a model set, if the inflation factor is a PV number [Mey95] .


Meyer, Y
Quasicrystals, Diophantine approximation and algebraic numbers
Beyond quasicrystals (Les Houches, 1994), Springer, Berlin 1995, MR1420415