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De Bruijn’s Pentagrids

In: A Guide to Penrose Tilings

Author

Listed:
  • Francesco D’Andrea

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

Abstract

This chapter is devoted to the methods and ideas introduced by Nicolaas G. de Bruijn, who provided some of the main contributions to the study of Penrose tilings. Here, we learn how to transform a regular pentagrid into a Penrose tiling. We discuss the cut-and-project method, first for one-dimensional tilings and then for Penrose tilings. We learn how to construct a Fibonacci tiling by projecting a portion of a 2-dimensional lattice on a line, and how to construct a tiling by Penrose rhombi by projecting a portion of a 5-dimensional lattice on a plane. We study how a pentagrid changes under Composition and classify the tilings associated with regular pentagrids.

Suggested Citation

  • Francesco D’Andrea, 2023. "De Bruijn’s Pentagrids," Springer Books, in: A Guide to Penrose Tilings, chapter 0, pages 121-155, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-28428-1_5
    DOI: 10.1007/978-3-031-28428-1_5
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