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Flat 2-Foldings of Convex Polygons

  • Conference paper
Combinatorial Geometry and Graph Theory (IJCCGGT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3330))

Abstract

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.

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References

  1. Demaine, E., Demaine, M., Lubiw, A., O’Rourke, J.: Enumerating foldings between polygons and polytopes. Graphs and Combinatorics 18(1), 93–104 (2002)

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  5. 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)

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Author information

Authors and Affiliations

  1. Research Institute of Educational Development Tokai University, Shibuya-ku, Tokyo, 151-8677, Japan

    Jin Akiyama

  2. Department of Mathematics, Faculty of Education, Ehime University, 3 Bunkyo-cho, Matsuyama, 790-8577, Japan

    Koichi Hirata

  3. Mathematics Department, School of Science and Engineering, Ateneo de Manila University, Quezon City, Philippines

    Mari-Jo P. Ruiz

  4. Instituto de Matemáticas, Universidad Nacionál Autónoma de México, México D.F., México

    Jorge Urrutia

Authors
  1. Jin Akiyama
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  2. Koichi Hirata
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  3. Mari-Jo P. Ruiz
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  4. Jorge Urrutia
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokio, Japan

    Jin Akiyama

  2. Department of Mathematics, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung, P.O. Box, 40132, Indonesia

    Edy Tri Baskoro

  3. Ibaraki University, Nakanarusawa, Hitachi, 316-8511, Ibaraki, Japan

    Mikio Kano

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© 2005 Springer-Verlag Berlin Heidelberg

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Akiyama, J., Hirata, K., Ruiz, MJ.P., Urrutia, J. (2005). Flat 2-Foldings of Convex Polygons. In: Akiyama, J., Baskoro, E.T., Kano, M. (eds) Combinatorial Geometry and Graph Theory. IJCCGGT 2003. Lecture Notes in Computer Science, vol 3330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30540-8_2

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  • DOI: https://doi.org/10.1007/978-3-540-30540-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24401-1

  • Online ISBN: 978-3-540-30540-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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