Polychromatic symmetry is a colour symmetry which interchanges three or more colours in a symmetrical pattern. It is a natural extension of dichromatic symmetry. The coloured symmetry groups are derived by adding to the position coordinates (x and y in two dimensions, x, y and z in three dimensions) an extra coordinate, k, which takes three or more possible values (colours).[1]
An example of an application of polychromatic symmetry is crystals of substances containing molecules or ions in triplet states, that is with an electronic spin of magnitude 1, should sometimes have structures in which the spins of these groups have projections of + 1, 0 and -1 onto local magnetic fields. If these three cases are present with equal frequency in an orderly array, then the magnetic space group of such a crystal should be three-coloured.[2][3]
- ^ Bradley, C.J. and Cracknell, A.P. (2010). The mathematical theory of symmetry in solids: representation theory for point groups and space groups, Clarendon Press, Oxford, 677–681, ISBN 9780199582587
- ^ Harker, D. (1981). The three-colored three-dimensional space groups, Acta Crystallogr., A37, 286-292, doi:10.1107/s0567739481000697
- ^ Mainzer, K. (1996). Symmetries of nature: a handbook for philosophy of nature and science, de Gruyter, Berlin, 162-168, ISBN 9783110129908