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- Metachirality abstract "Metachirality is a stronger form of chirality.It applies to objects or systems that are chiral (not identical to their mirror image) and where, in addition, their mirror image has a symmetry group that differs from the symmetry group of the original object or system.Many familiar chiral objects, like the capital letter 'Z' embedded in the plane, are not metachiral.The symmetry group of the capital letter 'Z' embedded in the plane consists of the identity transformation and a rotation over 180˚ (a half turn).In this case, the mirror image has the same symmetry group.In particular, asymmetric objects (that only have the identity transformation as symmetry, like a human hand) are not metachiral,since the mirror image is also asymmetric.In general, two-dimensional objects and bounded three-dimensional objects are not metachiral.An example of a metachiral object is an infinite helical staircase.A helix in 3D has a handedness (either left or right, like screw thread), whereby it differs from its mirror image.An infinite helical staircase, however, does have symmetries:screw operations, that is, a combination of a translation and a rotation.The symmetry group of the mirror image of an infinite helical staircase also contains screw operations.But they are of the opposite handedness and, hence,the symmetry groups differ.Note, however, that these symmetry groups are isomorphic.Of the 219 space groups, 11 are metachiral.A nice example of a metachiral spatial structure is the K4 crystal, also known as Triamond,and featured in the Bamboozle mathematical artwork.".
- Metachirality wikiPageID "41528945".
- Metachirality wikiPageLength "2631".
- Metachirality wikiPageOutDegree "21".
- Metachirality wikiPageRevisionID "679823386".
- Metachirality wikiPageWikiLink Asymmetry.
- Metachirality wikiPageWikiLink Category:Chirality.
- Metachirality wikiPageWikiLink Chirality.
- Metachirality wikiPageWikiLink Handedness.
- Metachirality wikiPageWikiLink Helix.
- Metachirality wikiPageWikiLink Identity_function.
- Metachirality wikiPageWikiLink Isomorphism.
- Metachirality wikiPageWikiLink Mirror_image.
- Metachirality wikiPageWikiLink Orientation_(vector_space).
- Metachirality wikiPageWikiLink Right-hand_rule.
- Metachirality wikiPageWikiLink Rotation.
- Metachirality wikiPageWikiLink Screw_axis.
- Metachirality wikiPageWikiLink Screw_thread.
- Metachirality wikiPageWikiLink Space_group.
- Metachirality wikiPageWikiLink Stairs.
- Metachirality wikiPageWikiLink Stereochemistry.
- Metachirality wikiPageWikiLink Symmetry_group.
- Metachirality wikiPageWikiLink Toshikazu_Sunada.
- Metachirality wikiPageWikiLink Translation.
- Metachirality wikiPageUsesTemplate Template:Reflist.
- Metachirality subject Category:Chirality.
- Metachirality hypernym Chiral.
- Metachirality type ChemicalCompound.
- Metachirality comment "Metachirality is a stronger form of chirality.It applies to objects or systems that are chiral (not identical to their mirror image) and where, in addition, their mirror image has a symmetry group that differs from the symmetry group of the original object or system.Many familiar chiral objects, like the capital letter 'Z' embedded in the plane, are not metachiral.The symmetry group of the capital letter 'Z' embedded in the plane consists of the identity transformation and a rotation over 180˚ (a half turn).In this case, the mirror image has the same symmetry group.In particular, asymmetric objects (that only have the identity transformation as symmetry, like a human hand) are not metachiral,since the mirror image is also asymmetric.In general, two-dimensional objects and bounded three-dimensional objects are not metachiral.An example of a metachiral object is an infinite helical staircase.A helix in 3D has a handedness (either left or right, like screw thread), whereby it differs from its mirror image.An infinite helical staircase, however, does have symmetries:screw operations, that is, a combination of a translation and a rotation.The symmetry group of the mirror image of an infinite helical staircase also contains screw operations.But they are of the opposite handedness and, hence,the symmetry groups differ.Note, however, that these symmetry groups are isomorphic.Of the 219 space groups, 11 are metachiral.A nice example of a metachiral spatial structure is the K4 crystal, also known as Triamond,and featured in the Bamboozle mathematical artwork.".
- Metachirality label "Metachirality".
- Metachirality sameAs Q17131155.
- Metachirality sameAs m.0_qcxj8.
- Metachirality sameAs Q17131155.
- Metachirality wasDerivedFrom Metachirality?oldid=679823386.
- Metachirality isPrimaryTopicOf Metachirality.