Big-little-big lemma
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In the mathematics of paper folding, the big-little-big lemma is a necessary condition for a crease pattern with specified mountain folds and valley folds to be able to be folded flat.[1] It differs from Kawasaki's theorem, which characterizes the flat-foldable crease patterns in which a mountain-valley assignment has not yet been made. Together with Maekawa's theorem on the total number of folds of each type, the big-little-big lemma is one of the two main conditions used to characterize the flat-foldability of mountain-valley assignments for crease patterns that meet the conditions of Kawasaki's theorem.[2] Mathematical origami expert Tom Hull calls the big-little-big lemma "one of the most basic rules" for flat foldability of crease patterns.[1]
The lemma concerns the angles made by consecutive pairs of creases at a single vertex of the crease pattern. It states that if any one of these angles is a local minimum (that is, smaller than the two angles on either side of it), then exactly one of the two creases bounding the angle must be a mountain fold and exactly one must be a valley fold.[1][2]