ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
This article contains a table of the groups of combined geometrical and color-permutational symmetry operations that leave a certain kind of three-colored, three-dimensionally periodic object apparently unchanged. The asymmetric units - 'motifs' - of the object are all either geometrically congruent to, or are mirror images of, one another. Each motif has a 'color' representing a scalar quality of some kind, and three different colors of motifs are assumed to occur in the object. Two types of three-colored space groups exist: type I in which all of the geometrical lattice translations leave all the motifs unchanged in color, and type II in which at least one of the geometrical lattice translations requires a permutation of the three colors in order to restore the original appearance. There are 88 three-colored space groups of type I, and 341 of type II. Type I can belong only to the trigonal, hexagonal and cubic systems; type II can belong to any system, except the cubic. A notation for the three-colored, three-dimensional space groups is proposed. It is based on similar principles to those used in the article on colored point groups by Harker [Acta Cryst. (1976), A32, 133-139].
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739481000697
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