Graphs and Combinatorics

, Volume 23, Supplement 1, pp 259–267

A Method to Generate Polyominoes and Polyiamonds for Tilings with Rotational Symmetry

  • Hiroshi Fukuda
  • Nobuaki Mutoh
  • Gisaku Nakamura
  • Doris Schattschneider
Article

DOI: 10.1007/s00373-007-0719-y

Cite this article as:
Fukuda, H., Mutoh, N., Nakamura, G. et al. Graphs and Combinatorics (2007) 23(Suppl 1): 259. doi:10.1007/s00373-007-0719-y

Abstract

We show a simple method to generate polyominoes and polyiamonds that produce isohedral tilings with p3, p4 or p6 rotational symmetry by using n line segments between lattice points on a regular hexagonal, square and triangular lattice, respectively. We exhibit all possible tiles generated by this algorithm up to n  =  9 for p3, n = 8 for p4, and n = 13 for p6. In particular, we determine for n ≤ 8 all n-ominoes that are fundamental domains for p4 isohedral tilings.

Keywords

Polyominoes Polyiamonds Isohedral tilings Rotational symmetry 

Copyright information

© Springer-Verlag Tokyo 2007

Authors and Affiliations

  • Hiroshi Fukuda
    • 1
  • Nobuaki Mutoh
    • 1
  • Gisaku Nakamura
    • 2
  • Doris Schattschneider
    • 3
  1. 1.School of Administration and InformaticsUniversity of ShizuokaShizuokaJapan
  2. 2.Research Institute of EducationTokai UniversityTokioJapan
  3. 3.Mathematics DepartmentPPHAC Moravian CollegeBethlehemUSA