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A New Kind of Symmetry

April 8, 2011

Rheanna Sand

Symmetry is so fundamental to our existence that we often need help to see it. Da Vinci's Vetruvian Man accentuated the beauty of bilateral symmetry the human form. Escher rotated and tessellated shapes to the point of mad genius. Mandelbrot coined the term fractal in 1975 and unknowingly invented the "trippy poster."

But now, a pair of Penn State researchers have defined a new type of symmetry itself - one that occurs in the crystalline lattice of solids. In an advanced online publication of Nature Materials, Venkatraman Gopalan and Daniel Litvin describe a new way of looking at crystals that may boost the efficiency and effectiveness of the search for new electronic and optic materials.

This new symmetry is called rotation reversal, and is added to the five types already known: rotation, inversion, rotation inversion, translation, and time reversal. I find these terms much more easily understood with the "tell it to me like I'm five" approach.

Rotational symmetry - you can spin it around a point, like a pizza:

 


 

Inversion - you can fold it in half, like a paper airplane:

 


 

Rotation inversion - you can hold it on the corners like a dice and spin it in your fingers:

 


 
Translation - you can shuffle it over, like an infinite fence:

 



Time reversal - if you run the "movie" backward, it looks the same as if you run it forward. This one involves magnetism and the spin of subatomic particles. I couldn't think of any five-year-old examples for this one.

But rotation reversal symmetry is more complex. You can't take this shape, for example, and fold it in half evenly anywhere. You can't turn it 90 degrees and get the same shape.


You also can't take the 3-D version, hold it in the corners like a dice, and spin it to get the same shape.

It's a new type of symmetry that involves tilting one way, then the other in an alternating fashion. The researchers think that materials with this property could be used as ultra-tiny on-off switches one day.

Did that just blow your mind or what?! Maybe they should think about going into the poster business...

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