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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/10308

Title: Common Developments of Several Different Orthogonal Boxes
Authors: Abel, Zachary
Demaine, Erik
Demaine, Martin
Matsui, Hiroaki
Rote, Günter
Uehara, Ryuhei
Keywords: Common Development
Origami
Issue Date: 2011
Magazine name: The 23rd Canadian Conference on Computational Geometry (CCCG' 11)
Start page: 77
End page: 82
Abstract: We investigate the problem of finding common developments that fold to plural incongruent orthogonal boxes. It was shown that there are infinitely many orthogonal polygons that fold to two incongruent orthogonal boxes in 2008. In this paper, we first show that there is an orthogonal polygon that fold to three boxes of size 1×1×5, 1×2×3, and 0×1×11. Although we have to admit a box to have volume 0, this solves the open problem mentioned in literature. Moreover, once we admit that a box can be of volume 0, a long rectangular strip can be folded to an arbitrary number of boxes of volume 0. We next consider for finding common non-orthogonal developments that fold to plural incongruent orthogonal boxes. In literature, only orthogonal folding lines orwith 45 degree lines were considered. In this paper, we show some polygons that can fold to two incongruent orthogonal boxes in more general directions.
Rights: Copyrights of the article is maintained by the authors. Zachary Abel, Erik Demaine, Martin Demaine, Hiroaki Matsui, Günter Rote and Ryuhei Uehara, The 23rd Canadian Conference on Computational Geometry (CCCG' 11), 2011, pp.77-82.
URI: http://hdl.handle.net/10119/10308
Material Type: author
Appears in Collections:b11-1. 会議発表論文・発表資料 (Conference Papers)

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