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

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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.

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Authors and Affiliations

  1. School of Administration and Informatics, University of Shizuoka, 52-1 Yada, Shizuoka, 422-8526, Japan

    Hiroshi Fukuda & Nobuaki Mutoh

  2. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokio, Japan

    Gisaku Nakamura

  3. Mathematics Department, PPHAC Moravian College, 1200 Main St, Bethlehem, PA, 18018-6650, USA

    Doris Schattschneider

Authors
  1. Hiroshi Fukuda
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  2. Nobuaki Mutoh
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  3. Gisaku Nakamura
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  4. Doris Schattschneider
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Fukuda, H., Mutoh, N., Nakamura, G. et al. A Method to Generate Polyominoes and Polyiamonds for Tilings with Rotational Symmetry. Graphs and Combinatorics 23 (Suppl 1), 259–267 (2007). https://doi.org/10.1007/s00373-007-0719-y

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  • DOI: https://doi.org/10.1007/s00373-007-0719-y

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