We present in this paper a generic algorithm to compute the skeleton of an n-dimensional binary object. Considering the cartesian hypercubic grid, we provide a mathematical framework in which are given the explicit Boolean conditions under which the iterative thinning procedure removes a point. This algorithm preserves the topology in a sense which matches the properties usually used in 2D and 3D. Furthermore, it is based on an original kind of median hypersurface that gives to the skeleton good behavior with respect to both shape preservation and noise sensitivity. The algorithm is fully parallel, as no spatial subiterations are needed. The latter property, together with the symmetry of the boolean n-dimensional patterns leads to a perfectly isotropic skeleton. The logical expression of the algorithm is extremely concise, and in 2D, a large comparative study shows that the overall number of elementary Boolean operations needed to get the skeleton is smaller than for the other iterative algorithms reported in the literature.