Overlapping Unit Cells in 3d Quasicrystal Structure

Details Overlapping Unit Cells in 3d Quasicrystal Structure Overlapping Unit Cells in 3d Quasicrystal Structure

2005-07-05

arxiv.org/abs/cond-mat/0507117v2

J. Phys. A: Math. Gen. 39 (2006) 9035-9044

Physics

Condensed Matter

Other Condensed Matter

LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final version

Scientific paper

10.1088/0305-4470/39/29/001

A 3-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 P, and 4 are interior points also shared with other neighboring unit cells. Using Kronecker's theorem the frequencies of all possible types of overlapping are found.

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