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Structural Relationships by Group-Subgroup Relations

As an example of the prevalence of high-symmetry structures we can take the closest packings of spheres only in the cubic and the hexagonal closest-packing of spheres are all atoms symmetry equivalent in other stacking variants of closest-packings several nonequivalent atomic positions are present, and these packings only seldom occur. [Pg.215]

The given conditions do not always allow for equivalent positions for all atoms. Take as an example the following conditions composition MX5, covalent M-X bonds, all X atoms bonded to M atoms. In this case all X atoms can only be equivalent if each set of five of them form a regular pentagon around an M atom (as for example in the XeFj ion). If this is not possible for some reason, then there must be at least two non-equivalent positions for the X atoms. According to the symmetry principle the number of these non-equivalent positions will be as small as possible. [Pg.215]

As was shown in various previous chapters, many structures of solids can be regarded as derivatives of simple, high-symmetry structure types. Let us recall some examples  [Pg.215]

Body-centered cubic sphere packing = CsCl type = superstructures of the CsCl type [Pg.215]

Closest-packings = closest-packings with occupied octahedral interstices (e.g. Cdl2 [Pg.215]


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Group structure

Group subgroup

Group-subgroup relations

Group-subgroup relationship

Related Structures

Subgroup

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