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

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

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]. View Full-Text
Keywords: polyominoes; polyiamonds; isohedral tilings; two-dimensional symmetry groups; fundamental domains 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.

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