Difference between revisions of "Symmetry operation"
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The two configurations/objects can be either congruent or enantiomorphous. Correspondingly, the symmetry operations are classed into two kinds: | The two configurations/objects can be either congruent or enantiomorphous. Correspondingly, the symmetry operations are classed into two kinds: | ||
* '''symmetry operations of first kind''': they relate congruent objects and consist of translations, rotations and screw rotations; | * '''symmetry operations of first kind''': they relate congruent objects and consist of translations, rotations and screw rotations; | ||
| − | * '''symmetry operations of second kind''': they relate enantiomorphous objects and consist of inversion, reflections, rotoinversions, and glide reflections. There exist a 1:1 correspondence between rotoinversion and rotoreflections: the latter are more used in Schoenflies notation, whereas rotoinversions are preferred in Hermann-Mauguin notation. | + | * '''symmetry operations of second kind''': they relate enantiomorphous objects and consist of inversion, reflections, rotoinversions, and glide reflections. There exist a 1:1 correspondence between rotoinversion and rotoreflections: the latter are more used in Schoenflies notation, whereas rotoinversions are preferred in [[Hermann-Mauguin symbols|Hermann-Mauguin]] notation. |
A symmetry operation can be performed about a [[symmetry element]]. Exceptions are the identity and the pure translations, for which a symmetry element is not defined. | A symmetry operation can be performed about a [[symmetry element]]. Exceptions are the identity and the pure translations, for which a symmetry element is not defined. | ||
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Revision as of 13:46, 24 November 2016
Opération de symétrie (Fr); Symmetrie-Operationen (Ge); Operación de simetría (Sp); Ooerazione di simmetria (It); 対称操作 (Ja).
A symmetry operation is an isometry, i.e. a transformation under which two objects, or two configurations or an object, are brought to coincide. A symmetry operation is a Euclidean mapping: to each point of the first configuration there corresponds a point of the second configuration, the distances between two points are kept by the transformation, as are the angles.
The two configurations/objects can be either congruent or enantiomorphous. Correspondingly, the symmetry operations are classed into two kinds:
- symmetry operations of first kind: they relate congruent objects and consist of translations, rotations and screw rotations;
- symmetry operations of second kind: they relate enantiomorphous objects and consist of inversion, reflections, rotoinversions, and glide reflections. There exist a 1:1 correspondence between rotoinversion and rotoreflections: the latter are more used in Schoenflies notation, whereas rotoinversions are preferred in Hermann-Mauguin notation.
A symmetry operation can be performed about a symmetry element. Exceptions are the identity and the pure translations, for which a symmetry element is not defined.