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Dualized Ammann-Kramer-Neri tiling

Fujita, Nobuhisa

Journal of physics. Conference series, 2023-03, Vol.2461 (1), p.12007 [Periódico revisado por pares]

Bristol: IOP Publishing

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  • Título:
    Dualized Ammann-Kramer-Neri tiling
  • Autor: Fujita, Nobuhisa
  • Assuntos: Apexes ; Crystallography ; Physics ; Self-similarity ; Tetrahedra ; Tiling
  • É parte de: Journal of physics. Conference series, 2023-03, Vol.2461 (1), p.12007
  • Descrição: Abstract Self-similarity is a key characteristic of quasicrystalline tilings. The similarity ratio can be an n -th power of the irrational scaling unit associated with the relevant non-crystallographic Bravais class, where n is a natural number (e.g., 1, 2, …). The Ammann-Kramer-Neri tiling is a famous quasicrystalline tiling with icosahedral symmetry based on acute and obtuse rhombohedra. It has however remained underexplored in view of its self-similarity, since any attempt to find substitution rules has by far been hindered by the large similarity ratio of no less than τ 3 , where τ is the golden mean. We hereby illustrate a new approach to tackle this issue by introducing an auxiliary tiling that combines the rhombohedral tiling and its crystallographic dual supported on the body-centre positions. The vertices of this “dualized” tiling arise from the cut through the same kind of acceptance domain as that of the rhombohedral tiling, namely rhombic triacontahedron, attached to every point of the six-dimensional body-centred icosahedral Bravais lattice. Eleven kinds of polyhedra, nine out of which are tetrahedra, are identified as prototiles. This new tiling admits self-similarity with τ being the similarity ratio.
  • Editor: Bristol: IOP Publishing
  • Idioma: Inglês
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