An irreducible rectangle tiling contains a spiral

Tomoe Motohashi*, Kouki Taniyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider a tiling of a square by finitely many tiles each of which is a rectangle. We do not assume that the tiles are mutually congruent. Such a tiling is called irreducible if for any two tiles the union of them is not a rectangle. A tiling is called generic if no four tiles meet in a point. A tilling is trivial if it has only one tile. A tile r in a generic tiling of a square is called a spiral if it is contained in the interior of the square and for each edge e of r there is a tile s adjacent to r such that the straight line containing e intersects the interior of s. We show that a nontrivial generic irreducible tiling of a square has a spiral.

Original languageEnglish
Pages (from-to)175-184
Number of pages10
JournalJournal of Geometry
Issue number1-2
Publication statusPublished - 2008 Dec 1


  • Spiral
  • Tiling

ASJC Scopus subject areas

  • Geometry and Topology


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