Symmetry of opposites: Antisymmetry (Q1345070)

In the Euclidean plane, let \(F\) be a geometric figure the parts of which have two different colours. If a reflection, rotation or translation (i.e., a symmetry operation) is combined with a colour change, \(F\) is mapped into an ``antisymmetric'' geometric figure \(F'\). This notion of antisymmetry can be generalized by replacing ``geometric figure'' and ``colour'' by other objects and properties, respectively. The article contains many examples (and beautiful pictures) of antisymmetry from geometry (antireflections, translational antisymmetry, two-dimensional space groups), chemistry (spectroscopy, crystallography, organic synthesis), art (Hungarian batik design; pictures by Brisse, Escher, Mamedov, Vasarely), commercial art and even literature.