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Foldings of Regular Polygons to Convex Polyhedra I: Equilateral Triangles

  • Jin Akiyama
  • Gisaku Nakamura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

Abstract

To fold a regular n-gon into a convex polyhedron is to form the polyhedron by gluing portions of the perimeter of the n-gon together, i.e. the n-gon is a net of the polyhedron. In this paper we identify all convex polyhedra which are foldable from an equilateral triangle.

Keywords

Equilateral Triangle Degenerate Case Convex Polyhedron Regular Polygon Regular Tetrahedron 
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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References

  1. 1.
    Akiyama, J., Nakamura, G.: Foldings of regular polygons to convex polyhedra II: Regular pentagons. J. Indones. Math. Soc (MIHMI) 9(2), 89–99 (2003)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Akiyama, J., Nakamura, G.: Foldings of regular polygons to convex polyhedra III: Regular hexagons and regular n-gons, n ≥ 7 (to appear in Thai Journal of Mathematics)Google Scholar
  3. 3.
    Alexander, R., Dyson, H., O’Rourke, J.: The foldings of a square to convex polyhedra. In: Akiyama, J., Kano, M. (eds.) JCDCG 2002. LNCS, vol. 2866, pp. 38–50. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Demaine, E.D., Demaine, M.L., Lubiw, A., O’Rourke, J.: Examples, counterexamples, and enumeration results for foldings and unfoldings between polygons and polytopes, Technical Report No. 069, Smith College, Northampton, MA (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jin Akiyama
    • 1
  • Gisaku Nakamura
    • 1
  1. 1.Research Institute of Educational DevelopmentTokai UniversityShibuya, TokyoJapan

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