Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry

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/sym3040828

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 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There are no isohedral tilings with p3m1, p4m, or p6m symmetry groups that have polyominoes or polyiamonds as fundamental domains. We display the algorithms’ output and give enumeration tables for small values of n. This expands earlier works [1,2] and is a companion to [3].

【 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.