2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100157Model sets play a fundamental role in structure analysis of quasicrystals. The diffraction diagram of a quasicrystal admits as symmetry group a finite group G, and there is a G-cluster C (union of orbits of G) such that the quasicrystal can be regarded as a quasiperiodic packing of interpenetrating copies of C. We present an algorithm which leads from any G-cluster C directly to a multi-component model set Q such that the arithmetic neighbours of any point x belonging to Q are distributed on the sites of the translated copy x+C of C. Our mathematical algorithm may be useful in quasicrystal physics.This is the revised version (19 pages, 3 figures) of a paper submitted to Journal of Geometry and Physics. Software for generating quasiperiodic discrete sets available at http://fpcm5.fizica.unibuc.ro/~ncotfasMathematical Physics52C23text