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Continuous Flattening of Convex Polyhedra

  • Jin-ichi Itoh
  • Chie Nara
  • Costin Vîlcu
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

Abstract

A flat folding of a polyhedron is a folding by creases into a multilayered planar shape. It is an open problem of E. Demaine et al., that every flat folded state of a polyhedron can be reached by a continuous folding process. Here we prove that every convex polyhedron possesses infinitely many continuous flat folding processes. Moreover, we give a sufficient condition under which every flat folded state of a convex polyhedron can be reached by a continuous folding process.

Keywords

Convex Polyhedron Folding Process Polyhedral Surface Leaf Edge Original Face 
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 2012

Authors and Affiliations

  • Jin-ichi Itoh
    • 1
  • Chie Nara
    • 2
  • Costin Vîlcu
    • 3
  1. 1.Faculty of EducationKumamoto UniversityJapan
  2. 2.Liberal Arts Education Center, Aso CampusTokai UniversityAsoJapan
  3. 3.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

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