Authors’ abstract: For a sample of points drawn uniformly from either the d-dimensional torus or the d-cube, \(d\geq 2\), we give limiting distributions for the largest of the nearest-neighbor links. For \(d\geq 3\) the behavior in the torus is proved to be different from the behavior in the cube. The results given also settle a conjecture of N. Henze [J. Appl. Probab. 19, 344-354 (1982; Zbl 0484.62034)] and throw light on the choice of the cube or torus in some probabilistic models of computational complexity of geometrical algorithms.