, Volume 9, Issue 4, pp 382–397 | Cite as

Tiling a polygon with parallelograms

  • Richard Kenyon


Given a simple polygon in the plane we devise a quadratic algorithm for determining the existence of, and constructing, a tiling of the polygon with parallelograms. We also show that any two parallelogram tilings can be obtained from one another by a sequence of “rotations,” and give a condition for the uniqueness of such a tiling. Three generalizations of this problem, that of tiling by a fixed set of triangles, a fixed set of trapezoids, or parallelogram tiling for polygonal regions with holes, are shown to be NP-complete.

Key words

Tiling NP-complete 


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Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • Richard Kenyon
    • 1
  1. 1.Institut FourierSaint-Martin d'HeresFrance

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