| Abstract: | The geometric and crystallographic ideas for cell models and tilings in non-periodic ordered structures are outlined. The basic concepts, among them the cell geometry and duality in a lattice are explained for the example of a one dimensional section through the root lattice A 2. The corresponding constructions for 3D icosahedral sections through the 6D face-centered hypercubic lattice, equivalent to the root lattice D 6, are described. Two different tilings, one with equivalent, one with three inequivalent vertex positions, are derived and discussed. |
