HIGHER-DIMENSIONAL APPROACH TO A UNIFIED GROWTH-MODEL FOR CRYSTALS, QUASI-CRYSTALS, AND MULTIPLY TWINNED PARTICLES

In this work the decahedral-recursive (DR) growth model, which generates both crystals and quasicrystals of all symmetries, is formulated in the context of the cut-projection method. In this approach all operations in the bigger-dimensional space are justified by physical laws in three dimensions. Although all competing geometrical models of quasicrystals can be formulated in this language, the most physically significant equilibrium structures are found to be those from the so-called random tiling. The similarities and differences between DR and other schema are presented and analyzed.