  Model 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.
