  Rotation-reversal symmetry was recently introduced to generalize the symmetry
classification of rigid static rotations in crystals such as tilted octahedra
in perovskite structures and tilted tetrahedral in silica structures. This
operation has important implications for crystallographic group theory, namely
that new symmetry groups are necessary to properly describe observations of
rotation-reversal symmetry in crystals. When both rotation-reversal symmetry
and time-reversal symmetry are considered in conjunction with space group
symmetry, it is found that there are 17,803 types of symmetry, called double
antisymmetry, which a crystal structure can exhibit. These symmetry groups have
the potential to advance understanding of polyhedral rotations in crystals, the
magnetic structure of crystals, and the coupling thereof. The full listing of
the double antisymmetry space groups can be found in the supplemental materials
of the present work and online at our website:
http://sites.psu.edu/gopalan/research/symmetry/
