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Penrose Tilings

In: A Guide to Penrose Tilings

Author

Listed:
  • Francesco D’Andrea

    (University of Naples Federico II, Department of Mathematics and Applications “Renato Caccioppoli”)

Abstract

In this chapter, we study two of the aperiodic protosets discovered by Penrose: one formed by a kite and a dart, and the other formed by golden rhombi. We use the preliminary study of Robinson triangles in Chap. 3 to prove several local and global properties of Penrose tilings. We discuss Conway worms and their relation to some one-dimensional non-periodic tilings called Fibonacci tilings. We discuss ribbons and their properties and prove, using ribbons, that tiles in a Penrose tiling can have only finitely many orientations. We discuss non-local properties of Penrose tilings and empires, and finally talk about the 3-coloring problem for a Penrose tiling.

Suggested Citation

  • Francesco D’Andrea, 2023. "Penrose Tilings," Springer Books, in: A Guide to Penrose Tilings, chapter 0, pages 85-120, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-28428-1_4
    DOI: 10.1007/978-3-031-28428-1_4
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