Overlapping unit cells in 3D quasicrystal structure

Helen Au-Yang; Jacques H.H. Perk

doi:10.1088/0305-4470/39/29/001

Overlapping unit cells in 3D quasicrystal structure

Helen Au-Yang^*, Jacques H.H. Perk

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Article number	001
Pages (from-to)	9035-9044
Number of pages	10
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	29
DOIs	https://doi.org/10.1088/0305-4470/39/29/001
Publication status	Published - 21 Jul 2006
Externally published	Yes

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10.1088/0305-4470/39/29/001

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title = "Overlapping unit cells in 3D quasicrystal structure",

abstract = "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.",

author = "Helen Au-Yang and Perk, {Jacques H.H.}",

year = "2006",

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AU - Perk, Jacques H.H.

PY - 2006/7/21

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AB - 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.

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DO - 10.1088/0305-4470/39/29/001

M3 - Article

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

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Overlapping unit cells in 3D quasicrystal structure

Abstract

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