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Discrete & Computational Geometry

, Volume 53, Issue 2, pp 445–465 | Cite as

A Computer Search for Planar Substitution Tilings with \(n\)-Fold Rotational Symmetry

  • Franz Gähler
  • Eugene E. Kwan
  • Gregory R. Maloney
Article

Abstract

We describe a computer algorithm that searches for substitution rules on a set of triangles, the angles of which are all integer multiples of \(\pi /n\). We find new substitution rules admitting \(7\)-fold rotational symmetry at many different inflation factors.

Keywords

Polygon Substitution Tiling Computer 

Mathematics Subject Classification

37B10 55N05 54H20 37B50 52C23 

Notes

Acknowledgments

The first and third authors were partly supported by the German Research Council (DFG), CRC 701. The third author was also partly supported by the Fields Institute during a research visit.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Franz Gähler
    • 1
  • Eugene E. Kwan
    • 2
  • Gregory R. Maloney
    • 3
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.Department of Chemistry and Chemical BiologyHarvard UniversityCambridgeUSA
  3. 3.School of Mathematics & StatisticsNewcastle UniversityNewcastle upon TyneUK

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