A classification of special points of quasilattices in two dimensions

A complete classification of the special points of octagonal, decagonal and dodecagonal quasilattices in two dimensions (2D) is presented. They are obtained by projecting the special points of the starting n-gonal lattice (n=8, 10 or 12) in 4D onto a 2D subspace. A set of equivalent special points of a quasilattice are located on the centres of a single kind of tile in the quasiperiodic tiling associated with the quasilattice; the point symmetry of the special points is identical to that of the tiles. They form a quasilattice with the same point symmetry as that of the original quasilattice. The new quasilattice is of a 'Bravais type' or 'non-Bravais type' according to whether the point symmetry group of the special points is identical to the full point symmetry group of the quasilattice or its true subgroup, respectively.