the cutting tip comprises a lateral face for aligned lateral positioning against a lateral alignment line with a tool holder housing , comprising an alignment snout with first and second lateral alignment surfaces that bear respectively against first and second lateral driving alignment surfaces and comprising , at some distance , a third lateral alignment surface for bearing against a third lateral driving alignment wall surface , two out of the first , second and third alignment surfaces being mutually inclined in such a way as to ensure alignment in a chosen position of travel with respect to the driving lateral wall surfaces opposite .