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Polyominoes and Polyiamonds as Fundamental Domains for Isohedral Tilings of Crystal Class D2
College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato, Sagamihara, Kanagawa 252-0373, Japan
School of Administration and Informatics, University of Shizuoka, 52-1 Yada, Shizuoka 422-8526, Japan
Mathematics Department PPHAC Moravian College, 1200 Main Street Bethlehem, 18018-6650 PA, USA
* Author to whom correspondence should be addressed.
Received: 15 March 2011; in revised form: 24 May 2011 / Accepted: 27 May 2011 / Published: 9 June 2011
Abstract: We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have pmm, pmg, pgg or cmm symmetry . These symmetry groups are members of the crystal class D2 among the 17 two-dimensional symmetry groups . We display the algorithms’ output and give enumeration tables for small values of n. This work is a continuation of our earlier works for the symmetry groups p3, p31m, p3m1, p4, p4g, p4m, p6, and p6m [3–5].
Keywords: polyominoes; polyiamonds; isohedral tilings; two-dimensional symmetry groups; fundamental domains
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Fukuda, H.; Kanomata, C.; Mutoh, N.; Nakamura, G.; Schattschneider, D. Polyominoes and Polyiamonds as Fundamental Domains for Isohedral Tilings of Crystal Class D2. Symmetry 2011, 3, 325-364.
Fukuda H, Kanomata C, Mutoh N, Nakamura G, Schattschneider D. Polyominoes and Polyiamonds as Fundamental Domains for Isohedral Tilings of Crystal Class D2. Symmetry. 2011; 3(2):325-364.
Fukuda, Hiroshi; Kanomata, Chiaki; Mutoh, Nobuaki; Nakamura, Gisaku; Schattschneider, Doris. 2011. "Polyominoes and Polyiamonds as Fundamental Domains for Isohedral Tilings of Crystal Class D2." Symmetry 3, no. 2: 325-364.