The process involved here sounds unwieldy, but is, in fact, quite simple: a material has a 6-fold rotation symmetry if the arrangement of its atoms remains unchanged when it is rotated by 60 degrees - ...

Ordered materials with 7-fold, 9-fold or 11-fold symmetries are never observed in nature. Researchers discovered the reason for this when they tried to impose a 7-fold symmetry on a layer of charged ...

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape. We are fond of saying things are symmetric, but what does ...

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems. For more than 50 years, mathematicians have ...