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- W2023755422 abstract "Infinite sphere packings give information about the structure but not about the shape of large dense sphere packings. For periodic sphere packings a new method was introduced in [W2], [W3], [Sc], and [BB], which gave a direct relation between dense periodic sphere packings and the Wulff-shape, which describes the shape of ideal crystals. In this paper we show for the classical Penrose tiling that dense finite quasiperiodic circle packings also lead to a Wulff-shape. This indicates that the shape of quasicrystals might be explained in terms of a finite packing density. Here we prove an isoperimetric inequality for unions of Penrose rhombs, which shows that the regular decagon is, in a sense, optimal among these sets. Motivated by the analysis of linear densities in the Penrose plane we introduce a surface energy for a class of polygons, which is analogous to the Gibbs—Curie surface energy for periodic crystals. This energy is minimized by the Wulff-shape, which is always a polygon and in certain cases it is the regular decagon, in accordance with the fivefold symmetry of quasicrystals." @default.
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- W2023755422 date "1999-04-01" @default.
- W2023755422 modified "2023-09-25" @default.
- W2023755422 title "Quasicrystals and the Wulff-Shape" @default.
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- W2023755422 doi "https://doi.org/10.1007/pl00009430" @default.
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