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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/11480

Title: Common Developments of Three Incongruent Orthogonal Boxes
Authors: Shirakawa, Toshihiro
Uehara, Ryuhei
Keywords: Common development
convex polyhedron
Issue Date: 2013
Publisher: World Scientific Publishing
Magazine name: International Journal of Computational Geometry and Applications
Volume: 23
Number: 1
Start page: 65
End page: 71
DOI: 10.1142/S0218195913500040
Abstract: We investigate common developments that can fold into several incongruent orthogonal boxes. It was shown that there are infinitely many orthogonal polygons that fold into two incongruent orthogonal boxes in 2008. In 2011, it was shown that there exists an orthogonal polygon that folds into three boxes of size 1 × 1 × 5, 1 × 2 × 3, and 0 × 1 × 11. However it remained open whether there exists an orthogonal polygon that folds into three boxes of positive volume. We give an affirmative answer to this open problem. We show how to construct an infinite number of orthogonal polygons that fold into three incongruent orthogonal boxes.
Rights: Electronic version of an article published as International Journal of Computational Geometry and Applications, 23(1), 2013, 65-71. DOI:10.1142/S0218195913500040. Copyright World Scientific Publishing Company, http://dx.doi.org/10.1142/S0218195913500040
URI: http://hdl.handle.net/10119/11480
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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