The most simple type of symmetry -- rotation symmetry -- is obvious, for example, when a square shape is rotated around its center point: the square shows its symmetrical character by looking exactly the same at four points during the rotation: at 90 degrees, 180 degrees, 270 degrees, and 360 degrees. Gopalan and Litvin say their new rotation-reversal symmetry is obvious, as well, if you know where to look.
The "eureka moment" of the discovery occurred when Gopalan recognized that the simple concept of reversing the direction of a spiral-shaped structure from clockwise to counterclockwise opens the door to a distinctly new type of symmetry. Just as a square shape has the quality of rotation symmetry even when it is not being rotated, Gopalan realized that a spiral shape has the quality of rotation-reversal symmetry even when it is not being physically forced to rotate in the reverse direction. Their further work with this rotation-reversal concept revealed many more structural symmetries than previously had been recognized in materials containing various types of directionally oriented structures. Many important biological molecules, for example, are said to be either "right handed" or "left handed," including DNA, sugars, and proteins.
"We found that rotation-reversal symmetry also exists in paired structures where the partner components lean toward each other, then away from each other in paired patterns symmetrically throughout a material," Gopalan said. These "tilting octahedral" struc
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