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- W2029211688 abstract "The 32 minimal general generator sets (MGGS) for the three-dimensional double space groups are provided; each MGGS has a very limited number of parameters that describe the translational parts of the space groups belonging to a crystal class. The method of construction is based on the algebraic defining relations of the abstract generators of the point groups. The equivalence or inequivalence criteria for the space groups with respect to lattice transformations are established by introducing the definite set {U} of the unimodular matrices that leaves a lattice type L of each crystal class G. Based on the set {U}, it will be shown that mere shifts of the lattice origin are necessary and sufficient to determine the inequivalence of almost all the space groups belonging to a crystal class of high symmetry. It is simpler to construct MGGS of higher symmetry than those of lower symmetry; this contrasts with the existing methods, which are based on the solvability of the space groups." @default.
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- W2029211688 date "1986-05-01" @default.
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- W2029211688 title "The 32 minimal general generator sets of 230 double space groups" @default.
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- W2029211688 doi "https://doi.org/10.1063/1.527106" @default.
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