2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58618The paper studies ways in which the sets of a partition of a lattice in $\RR^n$ become regular model sets. The main theorem gives equivalent conditions which assure that a matrix substitution system on a lattice in $\RR^n$ gives rise to regular model sets (based on $p$-adic-like internal spaces), and hence to pure point diffractive sets. The methods developed here are used to show that the $n-$dimensional chair tiling and the sphinx tiling are pure point diffractive.29 pages, 7 figuresMetric Geometry51F99text