TY - CHAP AB - We address the problem of covering ℝ n with congruent balls, while minimizing the number of balls that contain an average point. Considering the 1-parameter family of lattices defined by stretching or compressing the integer grid in diagonal direction, we give a closed formula for the covering density that depends on the distortion parameter. We observe that our family contains the thinnest lattice coverings in dimensions 2 to 5. We also consider the problem of packing congruent balls in ℝ n , for which we give a closed formula for the packing density as well. Again we observe that our family contains optimal configurations, this time densest packings in dimensions 2 and 3. AU - Edelsbrunner, Herbert AU - Kerber, Michael ED - Calude, Cristian ED - Rozenberg, Grzegorz ED - Salomaa, Arto ID - 3796 T2 - Rainbow of Computer Science TI - Covering and packing with spheres by diagonal distortion in R^n VL - 6570 ER -