Origami, the ancient Japanese art of paper folding, has been making a modern-day comeback. In recent years, it has inspired a wide range of academics, from architects to engineers to materials scientists, to explore ways of transforming flat sheets of listless material into three-dimensional, reconfigurable structures that can expand, contract and shapeshift in an instant.

Some of the results have been truly remarkable. Last year, Harvard researchers presented a 3-D structure inspired by a modular origami technique called snapology, which, if scaled up, could make it possible to fold a house-sized object into a block that would fit inside a backpack.

But like other so-called "architected materials," also known as metamaterials, the structures cannot be reconfigured after they're built, limiting their use. What's more, researchers do not know which origami shapes, of the myriad possibilities, are best for making architected materials.

Now some of the same Harvard researchers that explored the snapology technique have come up with a general computer model for linking multi-sided, three-dimensional building blocks to make intricate, shapeshifting structures. The model, reported in the journal Nature, quantifies all of the different ways that a particular structure can transform, depending on the building blocks used.

The computer model could be used like a blueprint to develop reconfigurable robots and buildings and could even deepen the understanding of chemical reactions.

"Through a collaboration with designers and mathematicians, we found a way to generalize these rules and quickly generate a lot of interesting designs," associated professor and senior author on the researcher paper, Katia Bertoldi, said in a press release.

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Bertoldi and her colleagues, including with former graduate student Johannes Overvelde, Chuck Hoberman, of the Harvard Graduate School of Design and James Weaver, a senior research scientist at the Wyss, developed their computer model using a few basic shapes, including triangular and hexagonal prisms.

From there, they created and assessed almost a million designs and select the ones with the desired, reconfigurable functions.

Once they settled on a few that looked interesting, they built working models of the structures using laser-cut cardboard and double-sided tape. Folding the three-dimensional objects along certain edges caused the entire object to change shape. The video of a few of these shapes is mesmerizing.

"Now that we've solved the problem of formalizing the design, we can start to think about new ways to fabricate and reconfigure these metamaterials at smaller scales, for example through the development of 3D-printed self actuating environmentally responsive prototypes," Weaver said.

Not limiting the discovery to their own team, the researchers made their algorithm available to the larger community with hopes that other scientists will use it to discovery shapes they did not.