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”.
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Notes
- 1.
It is published in his blog at http://www.iwa-masaka.jp/56290.html of Masaka Iwai who is the inventor of this puzzle.
- 2.
This answer is also listed in Masaka Iwai’s blog http://www.iwa-masaka.jp/56291.html.
- 3.
We take modulo n. That is, \(n+1\) is assumed to be 1.
- 4.
Also see the dual of a polyhedron appearing in Sect. 2.1.
- 5.
Voronoi diagram plays a very important role in computational geometry and has many applications. Therefore, international conferences on Voronoi diagram as the main theme are held regularly. If you search on the web, you can find many scripts that generate Voronoi diagrams. Figure 7.4 is generated by a script of Alex Beutel’s webpage (http://alexbeutel.com/webgl/voronoi.html).
- 6.
Dynamic programming is one of techniques of algorithms. It is briefly described as follows. We first define a solution in a recursive way. Then, instead of recursive calls, the algorithm constructs the solution in a table in the bottom-up manner.
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Uehara, R. (2020). Bumpy Pyramids Folded from Petal Polygons. In: Introduction to Computational Origami. Springer, Singapore. https://doi.org/10.1007/978-981-15-4470-5_7
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