Common Unfoldings of Polyominoes and Polycubes

  • Greg Aloupis
  • Prosenjit K. Bose
  • Sébastien Collette
  • Erik D. Demaine
  • Martin L. Demaine
  • Karim Douïeb
  • Vida Dujmović
  • John Iacono
  • Stefan Langerman
  • Pat Morin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)

Abstract

This paper studies common unfoldings of various classes of polycubes, as well as a new type of unfolding of polyominoes. Previously, Knuth and Miller found a common unfolding of all tree-like tetracubes. By contrast, we show here that all 23 tree-like pentacubes have no such common unfolding, although 22 of them have a common unfolding. On the positive side, we show that there is an unfolding common to all “non-spiraling” k-ominoes, a result that extends to planar non-spiraling k-cubes.

Keywords

Computational Geometry Boundary Edge Dual Graph Euler Tour Dyck Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Greg Aloupis
    • 1
  • Prosenjit K. Bose
    • 3
  • Sébastien Collette
    • 2
  • Erik D. Demaine
    • 4
  • Martin L. Demaine
    • 4
  • Karim Douïeb
    • 3
  • Vida Dujmović
    • 3
  • John Iacono
    • 5
  • Stefan Langerman
    • 2
  • Pat Morin
    • 3
  1. 1.Academia SinicaTaiwan
  2. 2.Université Libre de BruxellesBelgium
  3. 3.Carleton UniversityCanada
  4. 4.Massachusetts Institute of TechnologyUSA
  5. 5.Polytechnic Institute of New York UniversityUSA

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