We describe a general family of curved-crease folding tessellationsconsisting of a repeating "lens" motif formed by two convex curved arcs. Thethird author invented the first such design in 1992, when he made both a sketchof the crease pattern and a vinyl model (pictured below). Curve fittingsuggests that this initial design used circular arcs. We show that in fact thecurve can be chosen to be any smooth convex curve without inflection point. Weidentify the ruling configuration through qualitative properties that a curvedfolding satisfies, and prove that the folded form exists with no additionalcreases, through the use of differential geometry.
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