“it took me 30 years to put my finger on
the big flaw.” — JIM PAPADOPOULOS
Spiral symmetry
is turning heads

By Devin Powell

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 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 Penn 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 afterward. A snowflake has what’s called rotational 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 Read-ing who along with Gopalan reported the results in the April 3 Nature Materials.

During the late 19th century, scientists figured out that symmetries limit the number of ways atoms can be arranged into crystals, calculating 230 possible patterns. In the mid-20th century another kind of symmetry, time reversal, extended the number of possible arrangements in magnetic materials to 1,421. With Gopalan and Litvin’s ne w “rotation-reversal” symmetry, crystallographers now have 17,807 patterns to look for when trying to characterize a material’s 3-D structure.

“People have looked at certain materials and wondered why they have certain properties,” says Manfred Fiebig, a physicist at the University of Bonn in Germany. “Now they may be able to argue that it’s because of this new symmetry.”