Determination of densest ball packings under cubic crystallographic groups by computer

The famous unsolved KEPLER conjecture about the densest ball packing of the whole Euclidean space E³ with equal balls motivated the initiative of U. Sinogowitz who posed the problem to find the densest homogeneous ball packing under a given space group. The maximal density π/√(18) ≈ 0.74048 of the lattice-like ball packing occurs at other space groups as well. The author reports a computer algorithm, which determines the densest simple transitive ball packing for each cubic crystallographic space group. The author proves here the convergence and gives the results in Table 2 where the known exact data are indicated too. A complete algorithm for every orbit type is in progress.