Dichromatic symmetry

Dichromatic triangle illustrating colour symmetry

Dichromatic symmetry,[1] also referred to as antisymmetry,[2][3] black-and-white symmetry,[4] magnetic symmetry,[5] counterchange symmetry[6] or dichroic symmetry,[7] is a symmetry operation which reverses an object to its opposite.[8] A more precise definition is "operations of antisymmetry transform objects possessing two possible values of a given property from one value to the other."[9] Dichromatic symmetry refers specifically to two-coloured symmetry; this can be extended to three or more colours in which case it is termed polychromatic symmetry.[10] A general term for dichromatic and polychromatic symmetry is simply colour symmetry. Dichromatic symmetry is used to describe magnetic crystals and in other areas of physics,[11] such as time reversal,[12] which require two-valued symmetry operations.

  1. ^ Loeb, A.L. (1971). Color and Symmetry, Wiley, New York, ISBN 9780471543350
  2. ^ Shubnikov, A.V. (1951). Symmetry and antisymmetry of finite figures, Izv. Akad. Nauk SSSR, Moscow
  3. ^ Cite error: The named reference Colored Symmetry was invoked but never defined (see the help page).
  4. ^ Gévay, G. (2000). Black-and-white symmetry, magnetic symmetry, self-duality and antiprismatic symmetry: the common mathematical background, Forma, 15, 57–60
  5. ^ Tavger, B.A. (1958). The symmetry of ferromagnetics and antiferromagnetics, Sov. Phys. Cryst., 3, 341-343
  6. ^ Woods, H.J. (1935). The geometric basis of pattern design part I: point and line symmetry in simple figures and borders, Journal of the Textile Institute, Transactions, 26, T197-T210
  7. ^ Makovicky, E. (2016). Symmetry through the eyes of old masters, de Gruyter, Berlin, ISBN 9783110417050
  8. ^ Atoji, A. (1965). Graphical representations of magnetic space groups, American Journal of Physics, 33(3), 212–219, doi:10.1119/1.1971375
  9. ^ Mackay, A.L. (1957). Extensions of space-group theory, Acta Crystallogr. 10, 543-548, doi:10.1107/S0365110X57001966
  10. ^ Lockwood, E.H. and Macmillan, R.H. (1978). Geometric symmetry  , Cambridge University Press, Cambridge, 67-70 & 206-208 ISBN 9780521216852
  11. ^ Padmanabhan, H., Munro, J.M., Dabo, I and Gopalan, V. (2020). Antisymmetry: fundamentals and applications, Annual Review of Materials Research, 50, 255-281, doi:10.1146/annurev-matsci-100219-101404
  12. ^ Shubnikov, A.V. (1960). Time reversal as an operation of antisymmetry, Sov. Phys. Cryst., 5, 309-314