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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

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Received: 15 March 2011; in revised form: 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, updated 22 June 2011; original version uploaded 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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.

AMA Style

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.

Chicago/Turabian Style

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.


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