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- W2051267012 abstract "A group-theoretical method is presented that enables the derivation of the symmetry of any composite created by the superposition of two identical point groups. The invariant points of the two components are considered in coincidence and the composite symmetry is expressed as the intersection of two sets of symmetry operations. The first set contains the symmetry operations common in the components when their mutual disposition is taken into account, whereas in the second set belong the additional symmetry operations relating the two equivalent components. The existence of such symmetrizing operations is revealed particularly clearly by using the framework of two-coloured symmetry. Analytical expressions for the operations of each set are derived in terms of the mutual orientation of the two components and theorems are given for the determination of the composite point symmetry when the components are rotated relative to each other along a direction passing through their origin. The application of the methodology is demonstrated by considering particular examples and a table of all possible composite symmetry groups associated with superpositions of the 32 crystallographic point groups is given." @default.
- W2051267012 created "2016-06-24" @default.
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- W2051267012 date "1984-05-01" @default.
- W2051267012 modified "2023-09-26" @default.
- W2051267012 title "Composite symmetry formed by two identical point groups with common origin" @default.
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- W2051267012 doi "https://doi.org/10.1107/s0108767384000453" @default.
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