2000/09/30 by J. Vidal, Julien Vidal, Rémy Mosseri +1 · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Codimension #Combinatorics #Fibonacci number #Geometry #Icosahedral symmetry #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Pure mathematics #Quasicrystal #Quasicrystal Structures and Properties #Quasiperiodic function #Substitution tiling #X-ray Diffraction in Crystallography #cond-mat
paper · pdf · doi:10.1088/0305-4470/34/18/317
published as J. Phys. A 34, 3927 (2001) · 11 pages, 3 EPS figures, final version with minor changes
openalex publication_date 2001/04/27 · arxiv created 2001/05/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a geometrical description of new canonical d -dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2 d and rhombohedra in 3 d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.