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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 tetrahedra 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 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 supplementary materials of the present work and at http://sites.psu.edu/gopalan/research/symmetry/ .

Supporting information

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Portable Document Format (PDF) file https://doi.org/10.1107/S2053273313023176/pc5029sup1.pdf
Color Automorphisms of Double Antisymmetry

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Portable Document Format (PDF) file https://doi.org/10.1107/S2053273313023176/pc5029sup2.pdf
Using the Machine Readable File

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Portable Document Format (PDF) file https://doi.org/10.1107/S2053273313023176/pc5029sup3.pdf
secondPartOfSymbolGenerators

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Portable Document Format (PDF) file https://doi.org/10.1107/S2053273313023176/pc5029sup4.pdf
Full version of Figure 3

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Zip compressed file https://doi.org/10.1107/S2053273313023176/pc5029sup5.zip
DASG-Machine-Readable

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Zip compressed file https://doi.org/10.1107/S2053273313023176/pc5029sup6.zip
CDF with tutorial

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Portable Document Format (PDF) file https://doi.org/10.1107/S2053273313023176/pc5029sup7.pdf
Double Antisymmetry Space Groups


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