Sequentially Divisible Dissections of Simple Polygons

  • Jin Akiyama
  • Toshinori Sakai
  • Jorge Urrutia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2098)


A k-dissection D of a polygon P, is a partition of P into a set pf subpolygons {Q 1,...,Q m } with disjoint interiors such that these can be reassembled to form k polygons P 1,...,P k all similar to P. If for every j, 1 ≤ jk, the pieces of D can be assembled into j polygons, all similar to P, then D is called a sequentially k-divisible dissection. In this paper we show that any convex n-gon, n ≤ 5, has a sequentially k-divisible dissection with (k - 1)n+1 pieces. We give sequentially k-divisible dissections for some regular polygons with n ≥ 6 vertices. Furthermore, we show that any simple polygon P with n vertices has a (3k+4)-dissection with (2n - 2) +k(2n + ⌊ n/3 ⌋ - 4) pieces, k ≤ 0, that can be reassembled to form 4,7,..., or 3k + 4 polygons similar to P. We give similar results for star shaped polygons.


Problem Complexity Computer Graphic Algorithm Analysis Discrete Mathematic Regular Polygon 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jin Akiyama
    • 1
  • Toshinori Sakai
    • 2
  • Jorge Urrutia
    • 3
  1. 1.Research Institute of Educational DevelopmentTokai UniversityTokyoJapan
  2. 2.Research Institute of EducationTokai UniversityTokyoJapan
  3. 3.Instituto de MatemáticasCiudad Universitaria Universidad Nacional Autónoma de MéxicoMéxico D.F.México

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