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The fold-and-cut theorem states that any shape with straight sides can be cut from a single sheet of paper by folding it flat and making a single straight complete cut. Such shapes include polygons, which may be concave, shapes with holes, and collections of such shapes.
The corresponding problem that the theorem solves is known as the fold-and-cut problem, which asks what shapes can be obtained by the so-called fold-and-cut method. A particular instance of the problem, which asks how a particular shape can be obtained by the fold-and-cut method, is known as a fold-and-cut problem.
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