schoenflies

Schönflies (often spelled Schoenflies) refers to Theodor Schönflies, a German mathematician and crystallographer active in the late 19th and early 20th centuries. The name is attached to two widely used concepts in mathematics and chemistry: the Schönflies notation for point groups and the Schönflies theorem in topology.

Schönflies notation is a system for naming finite symmetry groups that describe the rotational and reflection symmetries of objects, particularly molecules. It classifies point groups with symbols such as Cn, Ci, Sn, Cnv, Dnh, Dnd, Oh, Td, and Ih, sometimes with subscripts or prefixes to indicate improper rotations or additional symmetry. The notation originated in Schönflies's work on crystallography and remains common in chemistry and spectroscopy, alongside the international Hermann–Mauguin notation.

In topology, the Schönflies theorem states that every simple closed curve in the plane can be mapped to a circle by a homeomorphism of the plane. Equivalently, the curve bounds a disk and the plane is partitioned into two regions each homeomorphic to a disk. The theorem is a foundational result in plane topology and has extensions and a generalization to higher dimensions known as the generalized Schoenflies problem.

Schönflies's work thus connects symmetry, geometry, and topology, and his notation remains a standard reference in molecular structure analysis and education.