Difference between revisions of "Symmetry operation"
From Online Dictionary of Crystallography
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| + | <font color="blue">Opération de symétrie</font> (''Fr''); <font color="red">Symmetrie-Operationen </font> (''Ge''); <font color="green">Operación de simetría</font> (''Sp''); <font color="black">Ooerazione di simmetria</font> (''It''); <font color="purple">対称操作</font> (''Ja''). | ||
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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. | 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. | ||
Revision as of 04:09, 20 March 2015
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.