Sümmeetriisus

Sümmeetriisus refers to the property of an object to map onto itself under a set of transformations, such as rotations, reflections, translations, or combinations. The term derives from the Estonian roots for symmetry (sümmeetri) and the suffix -isus, indicating a state or quality. In geometry and related fields, sümeetriisus is typically discussed in terms of a symmetry group: the collection of transformations that leave the object unchanged.

Objects can have varying sümeetriisus. A circle in the plane exhibits infinitely many symmetries: every rotation about its center and every reflection across a diameter maps the circle to itself. A square has eight symmetries (four rotations and four reflections), giving it a finite sümeetriisus. An equilateral triangle has six symmetries; a generic irregular shape has only the identity transformation, resulting in minimal sümeetriisus.

The concept is used in crystallography, computer vision, and art. Quantitative measures of sümeetriisus sometimes involve the size or structure of the symmetry group, or the extent to which a shape approximates an ideal symmetry under chosen transformations. In practice, researchers may analyze symmetric features, symmetry axes, and invariant descriptors to classify objects, detect patterns, or reduce complexity in modeling.

See also: symmetry, group theory, isometry, invariant.