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An object that is not chiral is said to be achiral. A chiral object and its mirror image are said to be enantiomorphs. The word chirality is derived from the Greek χείρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the Greek ἐναντίος (enantios) 'opposite' + μορφή (morphe) 'form'.
Conversely, a mirror image of an achiral object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called enantiomorphs (Greek, "opposite forms") or, when referring to molecules, enantiomers. A non-chiral object is called achiral (sometimes also amphichiral) and can be superposed on its mirror ...
A theory that is asymmetric with respect to chiralities is called a chiral theory, while a non-chiral (i.e., parity-symmetric) theory is sometimes called a vector theory. Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories.
The conjugacy definition would also allow a mirror image of the structure, but this is not needed, the structure itself is achiral. For example, if a symmetry group contains a 3-fold axis of rotation, it contains rotations in two opposite directions. (The structure is chiral for 11 pairs of space groups with a screw axis.)
The simplest chiral knot is the trefoil knot, which was shown to be chiral by Max Dehn. All nontrivial torus knots are chiral. The Alexander polynomial cannot distinguish a knot from its mirror image, but the Jones polynomial can in some cases; if V k ( q ) ≠ V k ( q −1 ), then the knot is chiral, however the converse is not true.
Any planar pattern that does not have a line of mirror symmetry is 2d-chiral, and examples include flat spirals and letters such as S, G, P. In contrast to 3d-chiral objects, the perceived sense of twist of 2d-chiral patterns is reversed for opposite directions of observation.
The full tetrahedral group T d with fundamental domain. T d, *332, [3,3] or 4 3m, of order 24 – achiral or full tetrahedral symmetry, also known as the (2,3,3) triangle group. This group has the same rotation axes as T, but with six mirror planes, each through two 3-fold axes. The 2-fold axes are now S 4 (4) axes.
D nd (or D nv), [2n,2 +], (2*n) of order 4n – antiprismatic symmetry or full gyro-n-gonal group (abstract group: Dih 2n). For a given n , all three have n -fold rotational symmetry about one axis ( rotation by an angle of 360°/ n does not change the object), and 2-fold rotational symmetry about a perpendicular axis, hence about n of those.