Chirality
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly can't be mapped to its mirror images by rotations and translations alone. Such objects then come in two forms, called enantiomorphs. The word Chirality is derived from the greek χειρ (cheir), the hand, the most familiar chiral object. A non-chiral figure is also called achiral.
A figure is achiral if and only if its symmetry group contains at least one indirect (orientation reversing) isometry.
Many familiar objects are chiral - for instance, a right glove and left glove are enantiomorphic, and so are the S and Z tetrominoes of the popular video game Tetris.
In three dimensions, every figure which possesses a plane of symmetry or a center of symmetry is achiral. (A center of symmetry of a figure is a point , such that is invariant under the mapping , where we have chosen to be the origin of the coordinate system.) Note, however, that there are achiral figures lacking both plane and center of symmetry.
In two dimensions, every figure which possesses a line of symmetry is achiral, and it can be shown that every bounded achiral figure must have a line of symmetry. Consider the following pattern:
> > > > > > > > > >
> > > > > > > > > >This figure is chiral, as it is not identical to its mirror image:
> > > > > > > > > >
> > > > > > > > > >But if one prolongs the pattern in both directions to infinity, one receives an (unbounded) achiral figure which has no line of symmetry.
Some molecules are chiral, for instance optical isomers, and their study is part of stereochemistry.
The fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears to violate even that symmetry.
Chirality appears to be important in particle physics because the universe seems to be asymmetric as far as spin is concerned. Imagine a particle moving in the direction of one's thumb. The particle can be classified as left-handed if it is spinning in the direction of the fingers of the left-hand and right-handed if it is spinning in the direction of the fingers of the right-hand. Up to now, only left-handed neutrinos (and right-handed anti-neutrinos) have been observed. But this is explained by the difficulty of detecting right-handed particles at extremely small masses.