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Folding polyominoes with holes into a cube
Computational Geometry ( IF 0.6 ) Pub Date : 2020-08-18 , DOI: 10.1016/j.comgeo.2020.101700
Oswin Aichholzer , Hugo A. Akitaya , Kenneth C. Cheung , Erik D. Demaine , Martin L. Demaine , Sándor P. Fekete , Linda Kleist , Irina Kostitsyna , Maarten Löffler , Zuzana Masárová , Klara Mundilova , Christiane Schmidt

When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.



中文翻译:

将带孔的多米诺骨牌折叠成立方体

什么时候可以将多米诺骨牌纸折叠成一个单位立方?先前的工作研究了树状的多胺,但是带孔的多胺仍然是一个有趣的开放问题。我们提出了一个具有一个或几个孔的多米诺骨牌折叠成立方体的充分条件,以及不能折叠立方体的条件。特别是,我们显示了除五个特殊的“基本”孔以外的所有孔都可保证可折叠性。

更新日期:2020-08-18
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