Enumeration of Polyominoes, Polyiamonds and Polyhexes for Isohedral Tilings with Rotational Symmetry

  • Hiroshi Fukuda
  • Nobuaki Mutoh
  • Gisaku Nakamura
  • Doris Schattschneider
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4535)

Abstract

We describe computer algorithms that can enumerate and display, for a given n > 0 (in theory, of any size), all n-ominoes, n-iamonds, and n-hexes that can tile the plane using only rotations; these sets necessarily contain all such tiles that are fundamental domains for p4, p3, and p6 isohedral tilings. We display the outputs for small values of n. This expands on earlier work [3].

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    Fukuda, H., Mutoh, N., Nakamura, G., Schattschneider, D.: A Method to Generate Polyominoes and Polyiamonds for Tilings with Rotational Symmetry. Graphs and Combinatorics (suppl. 23), 259–267 (2007)MathSciNetCrossRefMATHGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hiroshi Fukuda
    • 1
  • Nobuaki Mutoh
    • 2
  • Gisaku Nakamura
    • 3
  • Doris Schattschneider
    • 4
  1. 1.College of Liberal Arts and SciencesKitasato UniversityKanagawaJapan
  2. 2.School of Administration and InformaticsUniversity of ShizuokaShizuokaJapan
  3. 3.Research Institute of EducationTokai UniversityShibuya-ku TokioJapan
  4. 4.Mathematics Dept.PPHAC Moravian CollegeBethlehemUSA

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