Discrete & Computational Geometry

, Volume 55, Issue 4, pp 972–996 | Cite as

Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry

  • Jarkko Kari
  • Markus Rissanen


In this paper we prove the existence of quasiperiodic rhombic substitution tilings with 2n-fold rotational symmetry, for any n. The tilings are edge-to-edge and use \(\lfloor {\frac{n}{2}\rfloor }\) rhombic prototiles with unit length sides. We explicitly describe the substitution rule for the edges of the rhombuses, and prove the existence of the corresponding tile substitutions by proving that the interior can be tiled consistently with the given edge substitutions.


Substitution tiling Quasiperiodic Rotation symmetry Rhombic tiling 



We would like to thank Henna Helander for editing the images and Reino Niskanen for many helpful comments and suggestions. This research was supported during 2012 by a grant from the Kone Foundation.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland
  2. 2.HelsinkiFinland

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