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...

considerations. The point group symmetry of a molecule is defined by the presence or absence of 5 types of symmetry element. Symmetry axis: an axis around which...

a symmetry element is present throughout the reaction mechanism (reactant, transition state, and product), it is called a conserved symmetry element. Then...

through its center are all symmetry operations. Each symmetry operation is performed with respect to some symmetry element (a point, line or plane). In...

axes, and there is a central inversion symmetry. Th is isomorphic to T × Z2: every element of Th is either an element of T, or one combined with inversion...

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure...

exactly when folded in half. Symmetry is one class of patterns in nature whereby there is near-repetition of the pattern element, either by reflection or...

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an...

\end{aligned}}} Identity element: The identity element is ⁠ i d {\displaystyle \mathrm {id} } ⁠, as it does not change any symmetry a {\displaystyle a} when...

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the...

Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular...

spectroscopy, and allows one to easily detect the presence of this symmetry element by comparison of the IR and Raman spectra generated by the same molecule...

Geometric symmetry is a book by mathematician E.H. Lockwood and design engineer R.H. Macmillan published by Cambridge University Press in 1978. The subject...

possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection among its symmetries is called centrosymmetric...

transformation, it is said to have symmetry, and the transformation is called a symmetry operation. Glide-reflection symmetry is seen in frieze groups (patterns...

determined and the correlated symmetry is identified, all symmetry element operations associated to that correlated symmetry's point group are performed for...

uniquely determine the element of the symmetries of the square used to obtain those positions, and so the group of symmetries of a square is isomorphic...

loudness, timbre, sonic texture and spatial location. A 'parameter' is any element that can be manipulated (composed) separately from other elements or focused...

regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection...

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...

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...

has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular...

right-handed and left-handed threefold screw axes without there being a symmetry element taking one to the other. (Threefold screw axes also exist in sodium...

Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object...

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...

substituents. Ligands with a C2 symmetry element have been particularly popular, in part because the presence of such an element reduces the possible binding...

global symmetry. Local symmetry, the cornerstone of gauge theories, is a stronger constraint. In fact, a global symmetry is just a local symmetry whose...

the fusion of the symmetry operators has an element without an inverse, the corresponding symmetry is called a non-invertible symmetry. The above definitions...

non-equivalent axes and planes in a symmetrical fashion. The direction of a symmetry element corresponds to its position in the Hermann–Mauguin symbol. If a rotation...

polygon with h-fold rotational symmetry. For root systems, no root maps to zero, corresponding to the Coxeter element not fixing any root or rather axis...