Theory of color symmetry for periodic and quasiperiodic crystals

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Abstract

The author presents a theory of color symmetry applicable to the description and classification of periodic as well as quasiperiodic colored crystals. This theory is an extension to multicomponent fields of the Fourier-space approach of Rokhsar, Wright, and Mermin. It is based on the notion of indistinguishability and a generalization of the traditional concepts of color point group and color space group. The theory is applied toward (I) the classification of all black and white space-group types on standard axial quasicrystals in two and three dimensions; (II) the classification of all black and white space-group types in the icosahedral system; (III) the determination of the possible numbers of colors in a standard two-dimensional N-fold symmetric color field whose components are all indistinguishable; and (IV) the classification of two-dimensional decagonal and pentagonal n-color space-group types, explicitly listed for n≤25.

Original languageEnglish
Pages (from-to)1181-1218
Number of pages38
JournalReviews of Modern Physics
Volume69
Issue number4
DOIs
StatePublished - Oct 1997
Externally publishedYes

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