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On triangulating three-dimensional polygons

Abstract A three-dimensional polygon is triangulable if it has a non-self-intersecting triangulation which defines a simply-connected 2-manifold. We show that the problem of deciding whether a 3-dimensional polygon is triangulable is NP -complete. We then establish some necessary conditions and some sufficient conditions for a polygon to be triangulable, providing special cases when the decision problem may be answered in polynomial time.