A grinder/polisher apparatus is disclosed, the apparatus comprising first and second sets of grinding elements (2, 3) facing each other under an angle (α) thus forming between the sets of grinding elements a V-groove in which the cutting edge of a knife is insertable for movement upon grinding, wherein the grinding elements are supported in holders (5, 6). The grinding elements (2, 3) are pivotally arranged in the holders (5, 6) about axes (R, R′) the inclinations of which correspond with the opening angle (α) of the V-groove.