ickesymmetrisk

Ickesymmetrisk is a term used to describe a property of lacking symmetry under any nontrivial symmetry operation. In geometry, a figure or object is ickesymmetrisk if its symmetry group consists only of the identity transformation, meaning there is no reflection, rotation, or other transformation (beyond doing nothing) that maps it onto itself. Many natural and man-made objects are only approximately asymmetric, showing small deviations from symmetry rather than complete absence of it.

Geometric examples include scalene polygons and irregular shapes. In practical terms, an object is considered asymmetric if it has no axes, planes, or centers of symmetry, though real-world objects may exhibit near-symmetries due to measurement or manufacturing tolerances. In biology and chemistry, asymmetry is often functionally significant: chiral molecules are non-superimposable mirror images and lack certain symmetry elements, influencing interactions with other chiral environments. In physics and engineering, intentional asymmetry can be used to produce directional effects or to break certain conserved symmetries.

Mathematically, symmetry properties are analyzed through symmetry groups, which collect all transformations that leave an object invariant. An ickesymmetrisk object has a trivial symmetry group containing only the identity. The degree of asymmetry can be described or quantified by comparing the object with its transformed copies, or by counting absent symmetry elements such as planes, axes, or rotational symmetries.

Related concepts include symmetry, asymmetry, mirror plane, chirality, and group theory.