Symmetryrelated

Symmetryrelated is an adjective used to describe objects, states, or properties that are connected by a symmetry transformation within a given system. If two configurations can be mapped into each other by a symmetry operation of the system, they are symmetryrelated.

In mathematics, symmetryrelated elements arise from the action of a symmetry group G on a set X. The orbit of an element x under G comprises all elements symmetryrelated to x. If the action has degeneracy, multiple states are symmetryrelated.

In physics, symmetryrelated states share invariants such as energy, momentum, or charge due to symmetrical laws. For example, in a square, the four corners are related by rotations; these corners are symmetryrelated. In crystallography, symmetryrelated positions are related by space-group operations, and structures related by symmetry are considered equivalent.

In data management and chemistry, symmetryrelated entries indicate duplications or equivalents under the system's symmetry operations; recognizing them helps reduce redundancy. When cataloging molecules, symmetryrelated conformers are treated as the same underlying structure under the symmetry group.

See also: symmetry operation, group action, orbit, automorphism, degeneracy. Formal definition: let G act on X; x and y in X are symmetryrelated if there exists g in G with g·x = y.