Local color symmetry (Q1063693)

The theory of color symmetry deals with the task of assigning colors to a structure or pattern with symmetry group G so that each symmetry operation is associated consistently with a permutation of the colors; we say it is colored G-symmetrically. The author explained the basic theory in Color Symmetry and Group Theory [Discrete Math. 38, 273-296 (1982; Zbl 0474.20001)], including a development of ''compound color symmetry'' for the case when several sequences of regions are to be colored simultaneously. In this paper is treated the situation where the pattern has a collection of motifs, moved transitively by G, and a particular motif M has symmetry group K which contains symmetry operations which are not symmetries of the overall pattern (this is then true of each motif). Each motif is then subdivided into fundamental regions. The article discusses how to apply colors to these regions so that each motif is colored symmetrically (i.e. M is colored K-symmetrically) and the overall pattern is colored G-symmetrically as a compound coloring. For the case that \(K\cap G\) is trivial an analysis of colorings is given in terms of the direct product group \(K\times G\).