The isotropic algorithm is constructed for random close packing of equisized spheres with triply periodic boundary conditions. All previously published packing methods with periodic boundaries were kinetics-determined; i.e., they contained a densification rate as an arbitrary parameter. In contrast, the present algorithm is kinetic-independent and demonstrates an unambiguous convergence to the experimental results. To suppress crystallization, the main principles of our algorithm are (1) to form a contact network at an early stage and ( 2 ) retain contacts throughout the densification, as far as possible. The particles are allowed to swell by the numerical solution of the differential equations of densification. The RHS of these equations is calculated efficiently from a linear system by a combination of conjugate gradient iterations and exact sparse matrix technology. When an excessive contact occurs and one of the existing bonds should be broken to continue the densification, an efficient criterion based on multidimensional simplex geometry is used for searching the separating bond. The algorithm has a well-defined termination point resulting in a perfect contact network with the average coordination number six (for particle number N >> 1 ) and a system of normal reactions between the spheres maintaining the structure. These forces are the counterpart of the algorithm and can be used to calculate small elastic particle deformations in a granular medium. Extensive calculations are presented for 50 ~< N ~< 400 and demonstrate verygood agreement with theexperimental packing density (about 0.637 ) and structure.