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A comparison is made between incommensurate phases related with the well known Frendel-Kontorova problem, and amorphous structures, on the basis of a problem of conflict between different symmetries. This similarity leads to a fruitful comparison of solutions with the introduction of a 3-dimensional devil's staircase for the characterization of amorphous structures. Finally for amorphous structures which propagate an icosahedral symmetry, self similar properties are shown with evidence for a long-range propagation.
J.C.S. Lévy (1985) studied this question.