Continuous Flattening of Orthogonal Polyhedra

  • Erik D. Demaine
  • Martin L. Demaine
  • Jin-ichi Itoh
  • Chie NaraEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9943)


Can we flatten the surface of any 3-dimensional polyhedron P without cutting or stretching? Such continuous flat folding motions are known when P is convex, but the question remains open for nonconvex polyhedra. In this paper, we give a continuous flat folding motion when the polyhedron P is an orthogonal polyhedron, i.e., when every face is orthogonal to a coordinate axis (x, y, or z). More generally, we demonstrate a continuous flat folding motion for any polyhedron whose faces are orthogonal to the z axis or the xy plane.


Folding Continuous flattening Orthogonal polyhedra 


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 1
  • Jin-ichi Itoh
    • 2
  • Chie Nara
    • 3
    Email author
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.Faculty of EducationKumamoto UniversityKumamotoJapan
  3. 3.Meiji Institute for Advanced Study of Mathematical SciencesMeiji UniversityTokyoJapan

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