Symmetrical

Symmetrical is an adjective describing objects, patterns, or relationships that display symmetry, i.e., invariance under a set of transformations such as reflection, rotation, or translation. The term derives from Greek symmetria, meaning "commensurability of parts," via Latin.

In mathematics and science, symmetry refers to a property that remains unchanged under a transformation. An object with a line of symmetry has a mirror image across that line; one with rotational symmetry remains unchanged after a rotation about a point by a certain angle. The concept extends to strings, functions, and physical systems, and is central to group theory in abstract algebra.

Common forms include reflectional (mirror) symmetry, rotational symmetry, translational symmetry, and radial symmetry. Bilateral symmetry is common in animals; radial symmetry is seen in echinoderms and many flowers; regular polygons have multiple axes of symmetry.

In chemistry and crystallography, symmetry elements such as a mirror plane, a center of inversion, and rotation axes classify molecules and crystals. Symmetry influences physical properties, selection rules in spectroscopy, and pattern formation. In design and art, symmetry conveys balance and harmony, while asymmetry can convey dynamism.

Usage: both "symmetric" and "symmetrical" function as adjectives; "symmetric" is often preferred in technical or mathematical contexts, though both are common in general usage.