Abstract
In this chapter, we focus on the edge-unfolding of convex polyhedron. It is conjectured that we can always do that, however, it is not yet settled. Thus we focus on the unfolding that is realized by zipper.
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Notes
- 1.
This is a common theorem that there is always a person who marks a score higher or equal to the average score. It is intuitively trivial, but very powerful theorem when we show existence.
- 2.
I have asked directly to Dr. Greg Aloupis, the author of [Alo05], but his answer was “It is complicated”.
References
E.D. Demaine, J. O’Rourke, Geometric Folding Algorithms: Linkages, Origami (Cambridge University Press, Polyhedra, 2007)
E.D. Demaine, M.L. Demaine, A. Lubiw, A. Shallit, J.L. Shallit, Zipper unfoldings of polyhedral complexes, in Canadian Conference on Computational Geometry (CCCG 2010) (2010), pp. 219–222
G. Aloupis, E.D. Demaine, S. Langerman, P. Morin, J. O’Rourke, I. Streinu, G. Toussaint, Edge-unfolding nested polyhedral bands. Comput. Geometry 39, 30–42 (2008)
G. Aloupis, Reconfigurations of polygonal structure. Ph.D. thesis, School of Computer Science, McGill University (2005)
E.D. Demaine, M.L. Demaine, R. Uehara, Zipper unfoldability of domes and prismoids, in Canadian Conference on Computational Geometry (CCCG 2013) (2013), pp. 43–48
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Uehara, R. (2020). Zipper-Unfolding. In: Introduction to Computational Origami. Springer, Singapore. https://doi.org/10.1007/978-981-15-4470-5_8
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DOI: https://doi.org/10.1007/978-981-15-4470-5_8
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