This paper is first a brief survey on links between Geometry of Numbers and aperiodic crystals in Physics, viewed from the mathematical side. In a second part, we prove the existence of a canonical cut-and-project scheme above a (ssfgud set) self-similar finitely generated packing of (equal) spheres Λ in R n and investigate its consequences, in particular the role played by the Euclidean and inhomogeneous minima of the algebraic number field generated by the self-similarity on the Delone

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... t of the sphere packing. We discuss the isolation phenomenon. The degree d of this field divides the Z-rank of Z[Λ − Λ]. We give a lower bound of the Delone constant of a k-thin ssfgud sphere packing which arises from a model set or a Meyer set when d is large enough. 2000 Mathematics Subject Classification: 52C17, 52C23.