superposable

Superposable is an adjective used in geometry, chemistry and related disciplines to describe whether two objects can be made to coincide exactly through rigid motions. In geometry and kinematics, two figures or shapes are superposable if there exists a translation and a rotation that maps one onto the other; equivalently, they are congruent under a rigid motion. In three dimensions this includes all proper rotations and translations, and in practice it means the objects have the same size and form.

In chemistry, the term is often applied to molecules. A molecule is said to be superposable with its mirror image if the two are identical under some rigid motion; such molecules are considered achiral. If a molecule is not superposable with its mirror image, it is chiral and exists as non-superposable enantiomers. The concept helps explain optical activity and the behavior of chiral compounds in biological systems.

Examples include spheres and cubes, which are trivially superposable with congruent copies, whereas many organic molecules lacking symmetry are non-superposable to their mirror images. The term is sometimes used in computer vision and pattern recognition to describe the feasibility of matching shapes under rigid transformations.

See also: symmetry, congruence, chirality, mirror image, rigid motion, isometry.