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  2. Chirality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Chirality_(mathematics)

    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'.

  3. Point group - Wikipedia

    en.wikipedia.org/wiki/Point_group

    The four-dimensional point groups (chiral as well as achiral) are listed in Conway and Smith, [1] Section 4, Tables 4.1–4.3. Finite isomorphism and correspondences The following list gives the four-dimensional reflection groups (excluding those that leave a subspace fixed and that are therefore lower-dimensional reflection groups).

  4. Chirality - Wikipedia

    en.wikipedia.org/wiki/Chirality

    Instead, both effects can also occur when the propagation direction of the electromagnetic wave together with the structure of an (achiral) material form a chiral experimental arrangement. [10] [11] This case, where the mutual arrangement of achiral components forms a chiral (experimental) arrangement, is known as extrinsic chirality. [12] [13]

  5. Chirality (physics) - Wikipedia

    en.wikipedia.org/wiki/Chirality_(physics)

    A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality).The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality.

  6. Point groups in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Point_groups_in_three...

    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.)

  7. Chiral knot - Wikipedia

    en.wikipedia.org/wiki/Chiral_knot

    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.

  8. Chirality (chemistry) - Wikipedia

    en.wikipedia.org/wiki/Chirality_(chemistry)

    Chiral molecules are always dissymmetric (lacking S n) but not always asymmetric (lacking all symmetry elements except the trivial identity). Asymmetric molecules are always chiral. [6] The following table shows some examples of chiral and achiral molecules, with the Schoenflies notation of the point group of the molecule.

  9. Chiral media - Wikipedia

    en.wikipedia.org/wiki/Chiral_media

    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.