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Crystallography and the penrose pattern

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  • Mackay, Alan L.

Abstract

The Penrose pattern is a tiling of two-dimensional and of three-dimensional space by identical tiles of two kinds (acute and obtuse rhombi with α = 72° and 144° in two dimensions and acute and obtuse rhombohedra with α = 63.43° and 116.57° in three dimensions). The two-dimensional pattern is a section through that in three dimensions. When joining (or recursion) rules are prescribed, the pattern is unique and non-periodic. It has local five-fold axes and thus represents a structure outside the formalism of classical crystallography and might be designated a quasi-lattice.

Suggested Citation

  • Mackay, Alan L., 1982. "Crystallography and the penrose pattern," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 609-613.
    • Handle: RePEc:eee:phsmap:v:114:y:1982:i:1:p:609-613
    DOI: 10.1016/0378-4371(82)90359-4
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    Cited by:

    1. Elisa Prato, 2023. "Toric Quasifolds," The Mathematical Intelligencer, Springer, vol. 45(2), pages 133-138, June.
    2. Iovane, G., 2007. "Hypersingular integral equations, Kähler manifolds and Thurston mirroring effect in ϵ(∞) Cantorian spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1041-1053.
    3. Iovane, G. & Giordano, P., 2005. "Hypersingular integral equations, waveguiding effects in Cantorian Universe and genesis of large scale structures," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 879-896.

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