Continuous Flattening of Convex Polyhedra

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


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.


Convex Polyhedron Folding Process Polyhedral Surface Leaf Edge Original Face 
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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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