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Proceedings of the American Mathematical Society

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Some tilings of the plane whose singular points form a perfect set

Author: Marilyn Breen
Journal: Proc. Amer. Math. Soc. 89 (1983), 477-479
MSC: Primary 52A45; Secondary 05B45
MathSciNet review: 715870
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Abstract: Let $ \mathcal{J}$ be a tiling of the plane such that for every tile $ T$ of $ \mathcal{J}$ there correspond a tile $ T'$ of $ \mathcal{J}$ (not necessarily unique) and an integer $ k(T,T')$ (depending on $ T$ and $ T'$), $ 2 < k$, such that $ T$ meets $ T'$ in $ k(T,T')$ connected components. Then the set of singular points of $ \mathcal{J}$ is a nowhere dense, perfect set.

References [Enhancements On Off] (What's this?)

  • [1] B. Grünbaum and G. C. Shepard, Tilings and patterns, Freeman, San Francisco, Calif. (to appear). MR 992195 (90a:52027)
  • [2] Alain Valette, Tilings of the plane by topological disks, Geom. Dedicata 11 (1981), 447-454. MR 637919 (82m:05032)

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Article copyright: © Copyright 1983 American Mathematical Society

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