An apparatus for cutting products (46A, 46B), the apparatus comprising: a casing comprising a circumferential wall, a circumferential opening in the wall, an adjustable slice gate that partially closes the opening, and a slicing knife that defines a gate opening with the slice gate, a width of the gate opening being adjustable by positioning of the slice gate relative to the casing, the slicing knife being orientated parallel to an axis of the casing, the slicing knife, an interior surface of the wall, and an interior surface of the slice gate each defining a periodic pattern of rounded peaks and valleys, the periodic shapes of the interior surfaces (56, 58) of the casing and the slicing gate being aligned with each other, an impeller adapted for rotation within the casing about the axis thereof to cause products (46A, 46B) within the impeller to be held by centrifugal force against the wall of the casing, carried past the slicing knife, and produce a single slice from each individual product (46A, 46B) with each rotation of the impeller, each slice having a cross-sectional shape periodically varying in thickness consistent with the width of the gate opening to have parallel peaks and valleys, each sliced product having a wavelength as measured from peak-to-peak at oppositely-disposed surfaces of the slice; circular knives adapted to produce strips from each slice by forming parallel cuts, each parallel cut coinciding with a peak of the slice so that each strip has a width substantially identical to the wavelength of the slice from which the strip is produced; and crosscut knives adapted to produce reduced-size products from each strip by forming parallel cuts, each parallel cut being transverse to the peaks of the slice and perpendicular to the parallel cuts formed by the circular knifes so that each reduced-size product retains the width of the strip from which the reduced-size product was produced and has a length determined by the crosscut knifes, the apparatus characterised in that: the periodic shape of the slicing knife being shifted so that each peak of the slicing knife opposes a corresponding peak of the surface of the slice gate and the width of the gate opening periodically varies between a minimum gap defined by the distance between opposing peaks of the slice knife and the surface of the slice gate, and a maximum gap defined by the distance between opposing valleys of the slice knife and the surface of the slice gate. a casing comprising a circumferential wall, a circumferential opening in the wall, an adjustable slice gate that partially closes the opening, and a slicing knife that defines a gate opening with the slice gate, a width of the gate opening being adjustable by positioning of the slice gate relative to the casing, the slicing knife being orientated parallel to an axis of the casing, the slicing knife, an interior surface of the wall, and an interior surface of the slice gate each defining a periodic pattern of rounded peaks and valleys, the periodic shapes of the interior surfaces (56, 58) of the casing and the slicing gate being aligned with each other, an impeller adapted for rotation within the casing about the axis thereof to cause products (46A, 46B) within the impeller to be held by centrifugal force against the wall of the casing, carried past the slicing knife, and produce a single slice from each individual product (46A, 46B) with each rotation of the impeller, each slice having a cross-sectional shape periodically varying in thickness consistent with the width of the gate opening to have parallel peaks and valleys, each sliced product having a wavelength as measured from peak-to-peak at oppositely-disposed surfaces of the slice; circular knives adapted to produce strips from each slice by forming parallel cuts, each parallel cut coinciding with a peak of the slice so that each strip has a width substantially identical to the wavelength of the slice from which the strip is produced; and crosscut knives adapted to produce reduced-size products from each strip by forming parallel cuts, each parallel cut being transverse to the peaks of the slice and perpendicular to the parallel cuts formed by the circular knifes so that each reduced-size product retains the width of the strip from which the reduced-size product was produced and has a length determined by the crosscut knifes, the apparatus characterised in that: the periodic shape of the slicing knife being shifted so that each peak of the slicing knife opposes a corresponding peak of the surface of the slice gate and the width of the gate opening periodically varies between a minimum gap defined by the distance between opposing peaks of the slice knife and the surface of the slice gate, and a maximum gap defined by the distance between opposing valleys of the slice knife and the surface of the slice gate.