Continuous Blooming of Convex Polyhedra by Demaine, Erik D., Demaine, Martin L., Hart, Vi, Iacono, John, Langerman, Stefan, O'Rourke, Joseph

“…We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. …”
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Refold rigidity of convex polyhedra by Demaine, Erik D., Demaine, Martin L., Itoh, Jin-ichi, Lubiw, Anna, Nara, Chie, O'Rourke, Joseph

“…If the unfolding is restricted to cut only edges of the polyhedron, we identify several polyhedra that are “edge-refold rigid” in the sense that each of their unfoldings may only fold back to the original. …”
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A Generalization of the Source Unfolding of Convex Polyhedra by Demaine, Erik D., Lubiw, Anna

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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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Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm by Damian, Mirela, Demaine, Erik D., Flatland, Robin

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Zipper unfolding of domes and prismoids by Demaine, Erik D., Demaine, Martin L., Uehara, Ryuhei

“…We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap—of two classes of polyhedra. Such unfoldings could be implemented by a single zipper, so they are also known as zipper edge unfoldings. …”
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Zipper Unfoldings of Polyhedral Complexes by Demaine, Erik D., Demaine, Martin L., Lubiw, Anna, Shallit, Arlo, Shallit, Jonah L.

“…We explore which polyhedra and polyhedral complexes can be formed by folding up a planar polygonal region and fastening it with one zipper. …”
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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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Embedding Stacked Polytopes on a Polynomial-Size Grid by Demaine, Erik D., Schulz, Andre

“…Ziegler, and is the rst nontrivial subexponential upper bound on the long-standing open question of the grid size necessary to embed arbitrary convex polyhedra, that is, about effcient versions of Steinitz's 1916 theorem. …”
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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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