Penn State Live - Search for advanced materials aided by discovery of hidden symmetries

Penn State Live - Search for advanced materials aided by discovery of hidden symmetries: Before the publication of this paper, scientists and engineers had five different types of symmetries to use as tools for understanding the structures of materials whose building blocks are arranged in fairly regular patterns. Four types of symmetries had been known for thousands of years -- called rotation, inversion, rotation inversion and translation -- and a fifth type -- called time reversal -- have been discovered about 60 years ago. Now, researchers at Penn State University have added a new, sixth, type, called rotation reversal. As a result, the number of known ways in which the components of such crystalline materials can be combined in symmetrical ways has multiplied from no more than 1,651 before to more than 17,800 now...
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.