Difference between revisions of "Symmetry operation"
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| − | 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 | + | <font color="blue">Opération de symétrie</font> (''Fr''). <font color="red">Symmetrieoperation</font> (''Ge''). <font color="black">Operazione di simmetria</font> (''It''). <font color="purple">対称操作</font> (''Ja''). <font color="green">Operación de simetría</font> (''Sp''). |
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| + | 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: | 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 | + | * '''symmetry operations of second kind''': they relate enantiomorphous objects and consist of inversion, reflections, rotoinversions, and glide reflections. There exists 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 | + | 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]] | ||
Latest revision as of 09:18, 20 November 2017
Opération de symétrie (Fr). Symmetrieoperation (Ge). Operazione di simmetria (It). 対称操作 (Ja). Operación de simetría (Sp).
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 exists 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.