  Classical crystals are solid materials containing arbitrarily long periodic
repetitions of a single motif. In this paper, we study the maximal possible
repetition of the same motif occurring in beta-integers -- one dimensional
models of quasicrystals. We are interested in beta-integers realizing only a
finite number of distinct distances between neighboring elements. In such a
case, the problem may be reformulated in terms of combinatorics on words as a
study of the index of infinite words coding beta-integers. We will solve a
particular case for beta being a quadratic non-simple Parry number.
