A catalytic component consisting essentially of particles of MgCl.sub.2 impregnated by a transition-metal compound and up to an effective amount of an electron donor, wherein said particles have the form of essentially regular polyhedrons with six or eight faces in which the paired symmetrically opposite faces are essentially parallel, two of which faces are large and elongated and form the top face and the bottom face of a polyhedron such that on each of them the longest diagonal (D) is larger than the shortest distance (d) separating two opposite sides, which large elongated faces are surrounded essentially perpendicularly by the other essentially rectangular faces that form the sides of the said polyhedron, the length of the smaller side (e) of each of the said essentially rectangular faces being less than the shortest distance (d) separating the two opposite sides of the large elongated faces.