Deflating the pentagon

Erik D. Demaine, Martin L. Demaine, Thomas Fevens, Antonio Mesa, Michael Soss, Diane L. Souvaine, Perouz Taslakian, Godfried Toussaint

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we consider deflations (inverse pocket flips) of n-gons for small n. We show that every pentagon can be deflated after finitely many deflations, and that any infinite deflation sequence of a pentagon results from deflating an induced quadrilateral on four of the vertices. We describe a family of hexagons that deflate infinitely for a specific deflation sequence, yet induce no infinitely deflating quadrilateral. We also review the known understanding of quadrilateral deflation.

Original languageEnglish (US)
Title of host publicationComputational Geometry and Graph Theory - International Conference, KyotoCGGT 2007, Revised Selected Papers
Pages56-67
Number of pages12
DOIs
StatePublished - 2008
EventInternational Conference on Computational Geometry and Graph Theory, KyotoCGGT 2007 - Kyoto, Japan
Duration: Jun 11 2007Jun 15 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4535 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherInternational Conference on Computational Geometry and Graph Theory, KyotoCGGT 2007
CountryJapan
CityKyoto
Period6/11/076/15/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Demaine, E. D., Demaine, M. L., Fevens, T., Mesa, A., Soss, M., Souvaine, D. L., Taslakian, P., & Toussaint, G. (2008). Deflating the pentagon. In Computational Geometry and Graph Theory - International Conference, KyotoCGGT 2007, Revised Selected Papers (pp. 56-67). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4535 LNCS). https://doi.org/10.1007/978-3-540-89550-3-6