Self-similarity of quasilattices in two dimensions. II. The 'non-Bravais-type' n-gonal quasilattice

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Abstract
For pt.I see ibid., vol.22, p.193, (1989). Presents a systematic method of dividing an n-gonal lattice into identical sublattices which are also n-gonal lattices. A 'non-Bravais-type' n-gonal quasilattice in two dimensions is constructed with the projection method by assigning windows with different shapes, sizes and/or orientations to the sublattices; the symmetries and the orientations of the windows are determined by the relative point symmetries of the sublattices to the n-gonal lattice, and windows assigned to equivalent sublattices differ from one another only in their orientations. The sublattices are transformed among themselves by a volume-conserving linear transformation induced by a (complex) PV unit in the n-cyclotomic field. A necessary and sufficient condition for a PV unit to be a (complex) self-similarity ratio of a 'non-Bravais-type' quasilattice is presented. It is shown that every 'non-Bravais-type' n-gonal quasilattice has a self-similarity characterised by PV unit.

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