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A four dimensional description for the trigonal phase is presented. It hasbeen demonstrated that it is possible to model one dimensional quasiperiodicstructure with trigonal symmetry apart from recovering the Miller-Bravaisscheme for the description of hexagonal phases. A similar discussion on the twoclasses of decagonal phases having 10/m and 105 symmetries will be given. Thedistinction in the six dimensional models of the two classes of solids has beenpointed out. The zone rules for all the cases have been formulated. Thecritical comparison for the structural description of trigonal, decagonal andrelated phases in terms of higher dimension is made. The unification achievedin the higher dimensional structural models of various phases has beenemphasized. The importance of such models for the study of structural phasetransformation has been indicated.

Novel aspects of higher dimensional structural description of trigonal, pentagonal and their related phases