Schoenflies Notation: A Way to Name Shapes

Introduced by Arthur Moritz Schoenflies in his 1891 work 'Krystallsysteme und Krystallstructur', the notation was designed to categorize the 32 crystallographic point groups, later expanding to describe molecular symmetry.

The ammonia molecule (NH3) belongs to the C3v point group, indicating a three-fold rotation axis and three vertical mirror planes.

Schoenflies notation is a mathematical framework used to classify the symmetry of finite objects. It provides a concise nomenclature for point groups, which are sets of symmetry operations that leave at least one point fixed.

It is essential for determining selection rules in spectroscopy and understanding molecular orbitals. It provides a rigorous language for describing the spatial arrangement of atoms within a molecule.

The notation uses a letter (C, D, S, T, O, or I) to denote the primary symmetry type, followed by a subscript indicating the order of the principal rotation axis and the presence of mirror planes (h, v, or d).