Screwy symmetry

Molecular structures that tilt clockwise (orange) or counterclockwise (blue) have revealed a new kind of symmetry

Physicists have put a new twist on the humble corkscrew. Just as a butterfly appears identical to its mirror image, objects made of structures that tilt, twist or spiral possess a symmetry now recognized for the first time.
The new discovery is based on a mathematical operation that transforms a clockwise helix into a counterclockwise one, or vice versa.
"Normally, a helix flips when you put a mirror up to it," says Venkatraman Gopalan, a materials scientist at Pennsylvania State University in University Park. "We've developed a special kind of mirror with this math woven into it." Seen in this mirror, an object with a spiral shape will look just like itself.
This symmetry joins a list of other, long-known ways to move or manipulate an object and leave it looking the same afterwards. A snowflake has what's called rotation symmetry: Turn it 60 degrees, and its appearance doesn't change. A piece of wallpaper with a repeating pattern looks identical when moved a bit to the right or left, demonstrating translational symmetry.
"This new symmetry we're playing around with has not been taken into account up to now," says Daniel Litvin, a physicist at Penn State Berks in Reading and coauthor with Gopalan of an April 3 paper in Nature Materials. "It gives you a finer classification of materials."
Source: Science News