A tire tread band for medium/heavy duty motor-vehicles having circumferential grooves confining three pairs of respectively center, intermediate and shoulder ribs. Respective tread blocks are defined along the center and intermediate ribs and they are confined by transverse cuts. The center cuts impart a cusp-shaped end conformation and a hollow-shaped end conformation to the respective blocks, and the shapes of said end portions mutually match. The intermediate cuts run in the linear extension of the center cuts to give the respective blocks a rhomboidal configuration. The tire can be alternately associated with a driving axle or a driven axle, by merely reversing its direction of rotation, so that the following results are selectively achieved: an increase in the traction capability by the intermediate blocks or an increase in the directional capability as a result of the mutual wedging between the center blocks at the ground-contacting area.