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

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

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 al...

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Veröffentlicht in:Graphs and combinatorics 2007-06, Vol.23 (S1), p.259-267
Hauptverfasser: Fukuda, Hiroshi, Mutoh, Nobuaki, Nakamura, Gisaku, Schattschneider, Doris
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Geometry
Graph theory
Mathematics
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Zusammenfassung: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 [less than or equal to] 8 all n-ominoes that are fundamental domains for p4 isohedral tilings. [PUBLICATION ABSTRACT]
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-007-0719-y