  A four dimensional description for the trigonal phase is presented. It has
been demonstrated that it is possible to model one dimensional quasiperiodic
structure with trigonal symmetry apart from recovering the Miller-Bravais
scheme for the description of hexagonal phases. A similar discussion on the two
classes of decagonal phases having 10/m and 105 symmetries will be given. The
distinction in the six dimensional models of the two classes of solids has been
pointed out. The zone rules for all the cases have been formulated. The
critical comparison for the structural description of trigonal, decagonal and
related phases in terms of higher dimension is made. The unification achieved
in the higher dimensional structural models of various phases has been
emphasized. The importance of such models for the study of structural phase
transformation has been indicated.
