In geometry, a figure is chiral if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be achiral. In 3 dimensions, not all achiral objects have a mirror plane. For example, a 3-dimensional object with inversion centre as its only nontrivial symmetry operation is achiral but has no mirror plane. A chiral object and its mirror image are said to be enantiomorphs. The word chirality is derived from the Greek χείρ, the hand, the most familiar chiral object; the wordenantiomorph stems from the Greek ἐναντίος 'opposite' + μορφή 'form'. A non-chiral figure is called achiral or amphichiral.
Examples
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Z
Some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule. Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves and shoes. Right shoes differ from left shoes only by being mirror images of each other. In contrast thin gloves may not be considered chiral if you can wear them. The J, L, S and Z-shaped tetrominoes of the popular video gameTetris also exhibit chirality, but only in a two-dimensional space. Individually they contain no mirror symmetry in the plane.
In three dimensions, every figure that possesses a mirror plane of symmetryS1, an inversion center of symmetryS2, or a higher improper rotationSnaxis of symmetry is achiral. Note, however, that there are achiral figures lacking both plane and center of symmetry. An example is the figure which is invariant under the orientation reversing isometry and thus achiral, but it has neither plane nor center of symmetry. The figure also is achiral as the origin is a center of symmetry, but it lacks a plane of symmetry. Achiral figures can have a center axis.
In two dimensions, every figure which possesses an axis of symmetry is achiral, and it can be shown that every bounded achiral figure must have an axis of symmetry. For that reason, a triangle is achiral if it is equilateral or isosceles, and is chiral if it is scalene. 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 achiral figure which has no axis of symmetry. Its symmetry group is a frieze group generated by a single glide reflection.
Knot theory
A knot is called achiral if it can be continuously deformed into its mirror image, otherwise it is called a chiral knot. For example, the unknot and the figure-eight knot are achiral, whereas the trefoil knot is chiral.
