a certain operation, namely a rigid transformation, that can be applied to that object such, that the result is that same object occupying exactly the same space as it occupied before the transformation took place

a set of transformations that transform one object onto another object

a transformation of an entity which preserves the properties of the entity

Point-Group Symmetry Properties of a molecule describing how it can be transformed and still appear exactly the same. Point-group symmetry is a method of naming the combination of symmetry elements which a molecule has. Back to .

Informally, an object or structure is symmetrical (or equivalently, it has a symmetry) if it looks the same after a specific type of change is applied to it. The object or structure can be material, such as a person, crystal, quilt, floor tiles, or molecule, or it can be an abstract structure such as a mathematical equation or a series of tones (music). The nature of the change can be similarly diverse, ranging from such simple and intuitive operations as moving across a regularly patterned tile floor or rotating an eight-sided vase, to complex transformations of equations or in the way music is played.