The box to the section comprises a means of support (10, 12) for positioning a profile (2) into abutment in two planes of base (pb1 and pb2) which are secant, and which are preferably perpendicular, and at least the first guide means (100, 110) making it possible to guide a saw blade in a first plane of section (c1), which is fixed and secant with the planes of base (pb1 and pb2), and which defines an angle of the initial cutting (α), with respect to one (pb1 and pb2 of the two planes of base). The adjusting wedge (3a) is fitted on the carton to section (1a) and / or is movable with respect to the box to section (1a) and makes it possible, with respect to one (pb2) of the two planes of the base, with a profile (2) into abutment at least against the said adjusting wedge, so as to modify the cutting angle of the profile (2) by modifying the orientation of the profile (2) with respect to the first plane of section (c1).
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