On the Theory of a Non-Periodic Quasilattice Associated with the Icosahedral Group

Abstract

A quasilattice in the euclidean space E3 is generated by dualization of a hexagrid. The construction is based on a general theory of periodic and non-periodic space filling by projection from hypergrids. Global and local properties of the quasilattice are discussed, including the structure factor, the form and packing of the cells, and the point symmetry. The quasilattice is expected to give a description of quasicrystals without periodic order which have recently been found in experiments.