Quasicrystal-crystal transition in the dodecagonal phase

The quasicrystal-crystal transition in dodecagonal structures is studied in the case of a two-dimensional quasiperiodic tiling obtained by projecting a sixdimensional cubic lattice. By following the already proposed technique which consists of tilting the projection plane, we propose a decoration of the quasilattice which satisfies the hard-core condition and explains qualitatively some features of the electron diffraction patterns of the dodecagonal phase recently reported in a Bi-Mn alloy. It suggests that the quasicrystal-crystal transition in the dodecagonal phase occurs in a continuous fashion.