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Symmetry 2011, 3(2), 325-364; doi:10.3390/sym3020325
Article

Polyominoes and Polyiamonds as Fundamental Domains for Isohedral Tilings of Crystal Class D2

1,* , 2
,
2
,
2
 and
3
1 College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato, Sagamihara, Kanagawa 252-0373, Japan 2 School of Administration and Informatics, University of Shizuoka, 52-1 Yada, Shizuoka 422-8526, Japan 3 Mathematics Department PPHAC Moravian College, 1200 Main Street Bethlehem, 18018-6650 PA, USA
* Author to whom correspondence should be addressed.
Received: 15 March 2011 / Revised: 24 May 2011 / Accepted: 27 May 2011 / Published: 9 June 2011
(This article belongs to the Special Issue Symmetry in Theoretical Computer Science)
Download PDF [1457 KB, 22 June 2011; original version 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 [1]. These symmetry groups are members of the crystal class D2 among the 17 two-dimensional symmetry groups [2]. 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 polyominoes; polyiamonds; isohedral tilings; two-dimensional symmetry groups; fundamental domains
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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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.

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