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Most people associate origami with colorful cranes and decorative frogs, but the ancient Asian art of folding paper may be a whole lot more useful than that. Scientists have used it to make tiny robots and other self-folding 3D devices, for example. Now, a team of soft-matter physicists has invented a method for designing origami by essentially assembling puzzle pieces that encode the various points or vertices where folds meet. The approach could make designing folding robots much easier.
“It’s a big advance, and I’m pretty excited about it,” says Christian Santangelo, a theoretical physicist at Syracuse University in New York who was not involved in the work.
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Wadding up a sheet of paper is easy; making it fold is much harder. Imagine you dot the sheet with random points and connect them with straight lines to create quadrilaterals—shapes with four sides, potentially all of different lengths. That pattern is a potential origami, with each line representing a foldable crease. Meanwhile, each point represents a vertex at which four creases meet, the minimum needed for folding. However, most of those random patterns won’t fold. If fact, finding one that will is among the hardest computational problems, says Martin van Hecke, a physicist at Leiden University in the Netherlands and the research institute AMOLF in Amsterdam. “The chances are basically zero” that any random pattern will fold, he says.
So van Hecke, Scott Waitukaitis, a physicist at the Institute of Science and Technology Austria in Klosterneuburg, and colleagues invented a way to generate origami that are sure to fold. They started with a single vertex defined by the four angles between its creases. Then they generated three related vertices by reversing the order of the angles; replacing each angle with a number given by subtracting the original from 180°; or applying both steps. Finally,...
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