The main contribution of the present article consists of new 3D parallel and symmetric thinning schemes which have the following qualities: They are effective and sound, in the sense that they are guaranteed to preserve topology. This guarantee is obtained thanks to a theorem on critical kernels; They are powerful, in the sense that they remove more points, in one iteration, than any other symmetric parallel thinning scheme; They are versatile, as conditions for the preservation of geometrical features (e.g., curve extremities or surface borders) are independent of those accounting for topology preservation; They are efficient: we provide in this article a small set of masks, acting in the grid ℤ3, that is sufficient, in addition to the classical simple point test, to straight-forwardly implement them.