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Overlapping unit cells in 3D quasicrystal structure

Au-Yang, Helen; Perk, Jacques


A three-dimensional quasiperiodic lattice, with overlapping unit cells and periodic in one direction, is constructed using grid and projection methods pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are the vertices of a convex polytope , and 4 are interior points also shared with other neighbouring unit cells. Using Kronecker's theorem the frequencies of all possible types of overlapping are found.

CollectionsANU Research Publications
Date published: 2006
Type: Journal article
Source: Journal of Physics A: Mathematical and General
DOI: 10.1088/0305-4470/39/29/001


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