at least 50 to 70 and at most 70 to 99 of the at least approximately circular circumference of the cutting element 115 in order to achieve the desired circumferential length the number and or the arc length of the cutting edge sections 120 in corresponding embodiments of the invention in each case vary with the diameter of the cutting device 100 i e as explained with reference to the following examples a larger smaller nominal diameter and radius of the cutting device 100 in each case requires the arrangement of a correspondingly larger smaller number of cutting edge sections 120 and or a longer shorter arc length of the cutting edge sections 120 wherein two successive cutting edge sections 120 are located beside one another spaced apart by a recess 140 consequently the cutting device 100 having a plurality of cutting edge sections 120 has at least one recess 140 in an arrangement having a plurality of cutting edge sections 120 a multiplicity of cutting edge sections 120 are in simultaneous contact with the container covering 190 in the course of the cutting operation such that an opening piece of the container covering 190 is cut into sheared off at a plurality of points simultaneously the extensive number of cutting edge sections 120 in proportion.