# Flat 2-Foldings of Convex Polygons

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

## Keywords

Singular Point Interior Point Equilateral Triangle Convex Polygon Convex Polyhedron
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

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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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Akiyama, J., Nakamura, G.: Foldings of regular polygons to convex polyhedra I: Equilateral triangles. In: Proc. IJCCGT. LNCS. Springer, Heidelberg (2004) (to appear)Google Scholar
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Akiyama, J., Nakamura, G.: Foldings of regular polygons to convex polyhedra II: Regular pentagons. J. Indonesia Math. Soc. 9, 89–99 (2003)
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Akiyama, J., Nakamura, G.: Foldings of regular polygons to convex polyhedra III: Regular hexagons and regular n-gons, n ≥ 7 (to appear in Thai J. Math.)Google Scholar
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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)

© 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