Common Developments of Three Incongruent Orthogonal Boxes

• Shirakawa, Toshihiro

• Uehara, Ryuhei

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.

identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/11480

Journal

• International Journal of Computational Geometry and Applications

  International Journal of Computational Geometry and Applications 23 (1), 65-71, 2013

  World Scientific Publishing

Keywords

• Common development
• convex polyhedron

Details

• CRID: 1050564287491823488
• NII Article ID: 120005323060
• ISSN: 02181959
• Web Site: http://hdl.handle.net/10119/11480
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles