Mahadevan and his team have characterized a fundamental origami fold, or tessellation, that could be used as a building block to create almost any three-dimensional shape, from nanostructures to buildings.
The folding pattern, known as the Miura-ori, is a periodic way to tile the plane using the simplest mountain-valley fold in origami. It was used as a decorative item in clothing at least as long ago as the 15th century. A folded Miura can be packed into a flat, compact shape and unfolded in one continuous motion, making it ideal for packing rigid structures like solar panels. It also occurs in nature in a variety of situations, such as in insect wings and certain leaves.
“Could this simple folding pattern serve as a template for more complicated shapes, such as saddles, spheres, cylinders, and helices?” asked Mahadevan.
“We found an incredible amount of flexibility hidden inside the geometry of the Miura-ori,” said Levi Dudte, graduate student in the Mahadevan lab and first author of the paper. “As it turns out, this fold is capable of creating many more shapes than we imagined.”
Think surgical stents that can be packed flat and pop-up into three-dimensional structures once inside the body or dining room tables that can lean flat against the wall until they are ready to be used.
Optimal calculated origami tessellations and their physical paper analogues.
Geometry of generalized Miura-ori.