Point, line, or plane about which a molecule or crystal is symmetric
In chemistry and crystallography, a symmetry element is a point, line, or plane about which symmetry operations can take place. In particular, a symmetry element can be a mirror plane, an axis of rotation (either proper and improper), or a center of inversion.[1][2][3] For an object such as a molecule or a crystal, a symmetry element corresponds to a set of symmetry operations, which are the rigid transformations employing the symmetry element that leave the object unchanged. The set containing these operations form one of the symmetry groups of the object. The elements of this symmetry group should not be confused with the "symmetry element" itself. Loosely, a symmetry element is the geometric set of fixed points of a symmetry operation. For example, for rotation about an axis, the points on the axis do not move and in a reflection the points that remain unchanged make up a plane of symmetry.
^Robert G. Mortimer (10 June 2005). Mathematics for Physical Chemistry. Academic Press. pp. 276–. ISBN 978-0-08-049288-9.
^"Symmetry element". Online Dictionary of Crystallography. 2021-09-25. Retrieved 2021-09-25.
^Wolff, P.M. de; et al. (1989). "Definition of symmetry elements in space groups and point groups. Report of the International Union of Crystallography Ad-Hoc Committee on the Nomenclature of Symmetry". Acta Crystallographica Section A. 45 (7): 494–499. doi:10.1107/S0108767389002230. ISSN 0108-7673. Retrieved 2021-09-29.
crystallography, a symmetryelement is a point, line, or plane about which symmetry operations can take place. In particular, a symmetryelement can be a mirror...
considerations. The point group symmetry of a molecule is defined by the presence or absence of 5 types of symmetryelement. Symmetry axis: an axis around which...
center are all symmetry operations. Each symmetry operation is performed with respect to some symmetryelement (a point, line or plane). Symmetry operations...
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Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular...
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure...
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2-element group containing the identity operation and a single reflection, which occurs when the figure has only a single axis of bilateral symmetry, for...
spectroscopy, and allows one to easily detect the presence of this symmetryelement by comparison of the IR and Raman spectra generated by the same molecule...
global symmetry. Local symmetry, the cornerstone of gauge theories, is a stronger constraint. In fact, a global symmetry is just a local symmetry whose...
space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are...
transformation, it is said to have symmetry, and the transformation is called a symmetry operation. Glide-reflection symmetry is seen in frieze groups (patterns...
regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection...
isometry. An object without any symmetry has as its symmetry group the trivial group containing only this isometry (symmetry type C1). In a topological space...
related to the hexagonal dihedral symmetry family. It is an element of 9 of 28 convex uniform honeycombs: It is also an element of five four-dimensional uniform...
subset with element orders 2, 3, 4 and 6. There are four involutional groups: no symmetry (C1), reflection symmetry (Cs), 2-fold rotational symmetry (C2), and...
has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular...
of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property...
around every edge, it has Schläfli symbol {4,3,3} with hyperoctahedral symmetry of order 384. Constructed as a 4D hyperprism made of two parallel cubes...
the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory...
the unit cell of the structure. The unit cell completely reflects the symmetry and structure of the entire crystal, which is built up by repetitive translation...
loudness, timbre, sonic texture and spatial location. A 'parameter' is any element that can be manipulated (composed) separately from other elements or focused...
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