2008 - 2010
Study of Isohedral tilings by polyominoes and polyiamonds
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) Grant-in-Aid for Scientific Research (C)
- Grant number
- 20540127
- Japan Grant Number (JGN)
- JP20540127
- Authorship
- Principal investigator
- Grant amount
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- (Total)
- 2,210,000 Japanese Yen
- (Direct funding)
- 1,700,000 Japanese Yen
- (Indirect funding)
- 510,000 Japanese Yen
- Grant type
- Competitive
We described 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 symmetry groups p3m1, p4m, or p6m that have polyominoes or polyiamonds as fundamental domains. We display the algorithms' output and give enumeration tables for small values of n.
- Link information
- ID information
-
- Grant number : 20540127
- Japan Grant Number (JGN) : JP20540127
List of results of the research project
Narrowing down
Papers
3-
Symmetry, 3(4) 828-851, Dec 12, 2011 Peer-reviewedLead authorCorresponding author
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Symmetry, 3(2) 325-364, Jun 9, 2011 Peer-reviewedLead authorCorresponding author
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理系への数学(2008年6月号), 41(6) 55-60, Jun, 2008 Lead authorCorresponding author
Presentations
3-
The China-Japan Joint Conference on Computation Geometry, Graphs and Applications, Nov 3, 2010
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The 7th Japan Conference on Computational Geometry and Graphs, Nov 12, 2009
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The 7th Japan Conference on Computational Geometry and Graphs, Nov 11, 2009