Flat 2-Foldings of Convex Polygons

  • Jin Akiyama
  • Koichi Hirata
  • Mari-Jo P. Ruiz
  • Jorge Urrutia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)


A folding of a simple polygon into a convex polyhedron is accomplished by glueing portions of the perimeter of the polygon together to form a polyhedron. A polygon Q is a flat n -folding of a polygon P if P can be folded to exactly cover the surface of Qn times, with no part of the surface of P left over. In this paper we focus on a specific type of flat 2-foldings, flat 2-foldings that wrapQ ; that is, foldings of P that cover both sides of Q exactly once. We determine, for any n, all the possible flat 2-foldings of a regular n-gon. We finish our paper studying the set of polygons that are flat 2-foldable to regular polygons.


Singular Point Interior Point Equilateral Triangle Convex Polygon Convex Polyhedron 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jin Akiyama
    • 1
  • Koichi Hirata
    • 2
  • Mari-Jo P. Ruiz
    • 3
  • Jorge Urrutia
    • 4
  1. 1.Research Institute of Educational Development Tokai UniversityShibuya-ku, TokyoJapan
  2. 2.Department of Mathematics, Faculty of EducationEhime UniversityMatsuyamaJapan
  3. 3.Mathematics Department, School of Science and EngineeringAteneo de Manila UniversityQuezon CityPhilippines
  4. 4.Instituto de MatemáticasUniversidad Nacionál Autónoma de MéxicoMéxico D.F.México

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