Continuously Flattening Polyhedra Using Straight Skeletons by Demaine, Erik D., Demaine, Martin L., Itoh, Jin-ichi, Lubiw, Anna, Nara, Chie, O'Rourke, Joseph, Abel, Zachary Ryan

“…We show that our method solves the fold-and-cut problem for convex polyhedra in any dimension. As an additional application, we show how a limiting form of our algorithm gives a general design technique for flat origami tessellations, for any spiderweb (planar graph with all-positive equilibrium stress).…”
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On folding and unfolding with linkages and origami by Abel, Zachary Ryan

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Bumpy pyramid folding by Abel, Zachary Ryan, Demaine, Erik D., Demaine, Martin L., Ito, Hiro, Snoeyink, Jack, Uehara, Ryuhei

“…By Alexandrov’s theorem, the crease pattern is unique if it exists, but the general algorithm known for this theorem is pseudo-polynomial, with very large running time; ours is the first efficient algorithm for Alexandrov’s theorem for a special class of polyhedra. We also give a polynomial time algorithm that finds the crease pattern to produce the maximum volume triangulated polyhedron.…”
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Algorithms for Designing Pop-Up Cards by Abel, Zachary Ryan, Demaine, Erik D., Demaine, Martin L., Eisenstat, Sarah Charmian, Lubiw, Anna, Schulz, Andre, Souvaine, Diane L., Viglietta, Giovanni, Winslow, Andrew

“…We also show how to obtain a more efficient construction for the special case of orthogonal polygons, and how to make 3D orthogonal polyhedra, from pop-ups that open to 90°, 180°, 270°, or 360°.…”
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