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