More ways to tile with only one shape polygon

@article{Socolar2007MoreWT,  title={More ways to tile with only one shape polygon},  author={Joshua E. S. Socolar},  journal={The Mathematical Intelligencer},  year={2007},  volume={29},  pages={33-38},  url={https://api.semanticscholar.org/CorpusID:119365079}}
  • J. Socolar
  • Published1 March 2007
  • Mathematics
  • The Mathematical Intelligencer
ConclusionI have exhibited several types of monotiles with matching rules that force the construction of a hexagonal parquet. The isohedral number of the resulting tiling can be made as large as desired by increasing the aspect ratio of the monotile. Aside from illustrating some elegant peculiarities of the hexagonal parquet tiling, the constructions demonstrate three points.1.Monotiles with arbitrarily large isohedral number do exist;2.The additional topological possibilities afforded in 3D… 

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