Planar tilings by polyominoes, polyhexes, and polyiamonds
Abstract
Using computer programs, we enumerate and classify the tiling behavior of small polyominoes (n[less-than-or-equals, slant]9), polyhexes (n[less-than-or-equals, slant]7), and polyiamonds (n[less-than-or-equals, slant]10). For tiles that tile the Euclidean plane, we give diagrams illustrating how they tile. We also show several larger tiles whose minimal fundamental domain in any admitted (periodic) tiling is significantly larger than for any previously known tile.
- Publication:
-
Journal of Computational and Applied Mathematics
- Pub Date:
- February 2005
- Bibcode:
- 2005JCoAM.174..329R
- Keywords:
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- Polyomino;
- Polyhex;
- Polyiamond;
- Planar tiling;
- Fundamental domain;
- Large fundamental domain