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Bumpy Pyramids Folded from Petal Polygons

  • Ryuhei UeharaEmail author
Chapter
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Abstract

In this chapter, we consider a special set of polygons and convex polyhedra folded from it. After giving the (counterintuitive) answers to the puzzle given in this book, we consider the folding problem of (bumpy) pyramids folded from a special set of polygons called “petal polygons”.

References

  1. [AGS+89]
    A. Aggarwal, L.J. Guibas, J. Saxe, P.W. Shor, A linear-time algorithm for computing the voronoi diagram of a convex polygon. Discret. Comput. Geom. 4(1), 591–604 (1989)MathSciNetCrossRefGoogle Scholar
  2. [Aur87]
    F. Aurenhammer, Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16, 78–96 (1987)MathSciNetCrossRefGoogle Scholar
  3. [BCK+10]
    M. de Berg, O. Cheong, M. van Kreveld, M. Overmars, Computational Geometry: Algorithms and Applications (Springer, Berlin, 2010)zbMATHGoogle Scholar
  4. [BI08]
    A.I. Bobenko, I. Izmestiev, Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes (2008), arXiv:math.DG/0609447
  5. [DO07]
    E.D. Demaine, J. O’Rourke, Geometric Folding Algorithms: Linkages, Origami (Cambridge University Press, Polyhedra, 2007)CrossRefGoogle Scholar
  6. [Die96]
    R. Diestel, Graph Theory (Springer, Berlin, 1996)zbMATHGoogle Scholar
  7. [KPD09]
    D. Kane, G.N. Price, E.D. Demaine, A pseudopolynomial algorithm for Alexandrov’s theorem, in 11th Algorithms and Data Structures Symposium (WADS 2009), pp. 435–446. Lecture Notes in Computer Science vol. 5664 (Springer, 2009)Google Scholar
  8. [Sab98]
    I.K. Sabitov, The volume as a metric invariant of polyhedra. Discret. Comput. Geom. 20, 405–425 (1998)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.JAISTIshikawaJapan

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