In the last chapter, we looked at origami twists, which come in a wide variety of forms. Any convex polygon can be turned into a twist, simply by erecting parallel pleats, each emanating at the same angle from its side of the polygon. If the twist angle is constant, then the pattern folds flat isometrically (without regard to layer intersection); but when we take into account the possibility of self-intersection (and the need to avoid it), the possible crease assignments of the pleats and the polygon can get very complex indeed, with the possible assignments depending upon the twist angles, the central polygon angles, and the number and lengths of polygon sides. Despite the potential complexity, though, there is always a safe twist angle, α safe, below which every possible anto crease assignment can fold flat without self-intersection.