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

Symmetry

Hiroshi Fukuda¹  Chiaki Kanomata¹  Nobuaki Mutoh¹  Gisaku Nakamura¹ 

[1] ¹College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato, Sagamihara, Kanagawa 252-0373, Japan ²School of Administration and Informatics, University of Shizuoka, 52-1 Yada, Shizuoka 422-8526, Japan ³Mathematics Department PPHAC Moravian College, 1200 Main Street Bethlehem, 18018-6650 PA, USA

关键词: polyominoes;    polyiamonds;    isohedral tilings;    two-dimensional symmetry groups;    fundamental domains;   

DOI  :  10.3390/sym3020325

来源: mdpi

【 摘 要 】

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].

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.