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The two principal systems of lattice constants that have arisen in the study of cooperative phenomena and related problems on crystal lattices are the strong (low-temperature) and the weak (high-temperature) systems. The two systems are defined in terms of the concepts of graph theory, and a general theorem relevant to cluster expansions is stated. The interrelation of the two systems is studied and exploited to derive configurational data for the face-centered cubic lattice. All star graphs with up to seven points (vertices) or nine lines (edges) that are embeddable on the face-centered cubic are described. A general classification of stars with cyclomatic index 3 is given.
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Sykes et al. (1966) studied this question.
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