2Symmetrie

2Symmetrie refers to twofold symmetry, an arrangement property describing invariance under a specific transformation whose square is the identity. In mathematical terms it is called an involution: applying the transformation twice returns the original object. The concept is central to areas such as geometry, algebra, and crystallography.

In plane geometry the typical realizations of 2Symmetrie are a 180-degree rotation about a fixed point or a reflection across a line. Both transformations, when applied twice, restore the original figure. An object may possess a single 2Symmetrie or multiple such symmetries that together influence its overall symmetry group.

More generally, an object has 2Symmetrie if its symmetry group contains an element of order 2, generating a cyclic group isomorphic to C2. In three dimensions a twofold axis, meaning a rotation by 180 degrees about an axis, is a common form of 2Symmetrie. Many molecules in chemistry and materials science exhibit C2 symmetry, and this property can influence physical behavior and spectroscopy.

In algebraic contexts a function or map that is its own inverse (f composed with f equals the identity) is an involution, embodying the idea of 2Symmetrie. In design, architecture and tiling, twofold symmetry is used to create balanced patterns that are invariant under a 180-degree rotation or reflection.

Overall, 2Symmetrie describes the simplest nontrivial symmetry beyond identity and provides a foundational concept across mathematics, science and the arts.