From patterns to space groups and the eigensymmetry of crystallographic orbits: a reinterpretation of some symmetry diagrams in IUCr Teaching Pamphlet No. 14
The space group of a crystal pattern is the intersection group of the eigensymmetries of the crystallographic orbits corresponding to the occupied Wyckoff positions. Polar space groups without symmetry elements with glide or screw components smaller than 1/2 do not contain characteristic orbits and cannot be realized in patterns (structures) made by only one crystallographic type of object (atom). The space-group diagram of the general orbit for this type of group has an eigensymmetry that corresponds to a special orbit in a centrosymmetric supergroup of the generating group. This fact is often overlooked, as shown in the proposed solution for Plates (i)–(vi) of IUCr Teaching Pamphlet No. 14, and an alternative interpretation is given.
2002 ◽
Vol 35
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pp. 368-370
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2001 ◽
Vol 57
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pp. 599-601
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2001 ◽
Vol 57
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pp. 471-484
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2007 ◽
Vol 62
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pp. 1235-1245
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1999 ◽
Vol 55
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pp. 607-616
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2021 ◽
Vol 77
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pp. 187-191
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Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces
2017 ◽
Vol 73
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pp. 387-402
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