The invention relates to a folding die (1) of a sheet metal part (4) for a folding machine. The matrix comprises two supports (2, 3) distant from each other to allow the folding of said part between these supports, and two rollers (5, 6) mounted in pivot connection on the supports with a spacing between these rollers allowing the sheet metal part to bear on said rollers during folding. The matrix makes it possible to increase the folding and counter-folding capacities of the pieces by increasing the radii of curvature, and reduces the degradation of the piece during its folding. The rollers (5, 6) are removable from the supports, said folding die comprising at least one pair of rings (21) configured to be added to the rollers (5, 6) so as to reduce the spacing between these rollers, the sheet metal part supported on the rings (211, 212, 213, 214).
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