The intimate relationship between the Penrose and the Taylor-Socolar tilings is studied, within both the context of double hexagon tiles and the algebraic context of hierarchical inverse sequences of triangular lattices. This unified approach produces both types of tilings together, clarifies their relationship and offers straightforward proofs of their basic properties.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5406916 | PMC |
| http://dx.doi.org/10.1107/S2053273317003576 | DOI Listing |
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On the Penrose and Taylor-Socolar hexagonal tilings.
Acta Crystallogr A Found Adv
May 2017
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada.
The intimate relationship between the Penrose and the Taylor-Socolar tilings is studied, within both the context of double hexagon tiles and the algebraic context of hierarchical inverse sequences of triangular lattices. This unified approach produces both types of tilings together, clarifies their relationship and offers straightforward proofs of their basic properties.
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