Erik and Martin Demaine created “Natural Cycles” as part of their exploration of curved folds in origami. They took a two-foot by two-foot piece of paper and cut the corners off to form an octagon. Then they creased concentric octagons within it with alternating folds. They dampened the paper, pressed all the folds at once, and put the edges of the paper in the shape of the cube’s Hamilton cycle. The combination of straight edges and straight folds formed a beautiful curved surface.