unsymmetric

Unsymmetric, also spelled unsymmetrical, is an adjective describing the lack of symmetry in an object, system, or relation. In common usage, it contrasts with symmetric or symmetrical.

In mathematics and computing: In linear algebra, an unsymmetric matrix is a matrix A for which A^T ≠ A. This includes most general matrices; symmetric matrices are the special case with A^T = A. Many numerical methods exploit symmetry for efficiency, while unsymmetric problems may require different algorithms, such as LU decomposition rather than Cholesky.

In geometry and design: A figure without any symmetry axes or centers is described as unsymmetric; it does not have reflectional, rotational, or translational symmetry by standard definitions. Irregular shapes may be unsymmetric.

In chemistry and materials science: The term describes molecules or crystal structures that lack symmetry elements such as mirror planes or rotation axes. In practice, many discussions distinguish symmetry from chirality, with asymmetric or enantioselective approaches often emphasized in synthesis and crystallography.

In biology and other fields, unsymmetric usage is less common than asymmetric, which more precisely conveys left–right differences or developmental disparities. Nevertheless, unsymmetric can appear in broad descriptions of processes or structures that do not exhibit symmetry, especially in historical or cross-disciplinary texts.

Related terms include symmetry, asymmetry, non-symmetric. The choice between symmetric, asymmetric, and unsymmetric often depends on the disciplinary convention and the specific context of the discussion.