The vacancy-ordered phases known as τ-phases were described, and published results on the stacking sequences observed were reviewed. It was shown that the stacking sequences along the 3-fold axis could be derived from a projection method which involved projection onto an axis of type, [rrq]. The structure had alternating filled and empty lamellae parallel to planes of type, (rrq). The particular cases in which r and q were consecutive numbers of the Fibonacci sequence could be regarded as rational approximants to a 1-dimensional quasi-periodic structure. Mathematical properties of the sequences, and their relationship to 3-dimensional structures, were presented.

Stacking Sequences and Symmetry Properties of Trigonal Vacancy-Ordered Phases (τ Phases). E.A.Lord, S.Ranganathan, A.Subramaniam: Philosophical Magazine A, 2002, 82[2], 255-68