AI 中文总结
该研究通过计算机搜索，发现了40个可折叠成三种不同表面积为106的长方体的多米诺网，还得到了相关无限网族及算法等结果，并提出了开放问题。
AI 中文摘要
我们通过计算机搜索获得了可折叠成2种和3种不同长方体的多米诺网的新结果。主要结果是发现了40个可折叠成三种不同长方体且表面积为106的多米诺网；次要结果包括发现了可折叠成三种长方体形状的无限多米诺网族，以及计算了较小长方体之间的公共网数量。为使搜索可行所使用的算法也将被说明，这些算法包括：利用可折叠成N×1×1长方体的网中的某些隐藏结构，利用大量网以“条纹状”方式折叠成长方体形状的特性，以及使用Redelmeier算法的变体。论文最后提出了开放问题，以鼓励读者拓展我们对多米诺网构造这一主题的整体理解。
英文摘要
We present new results for polyomino nets that fold into 2 and 3 different cuboids through a computer search. The main result is the finding of 40 nets that fold into all three different cuboids with a surface area of 106. The secondary results are the finding of infinite families of nets that fold into three cuboid shapes, and the calculation of the number of common nets between smaller cuboids. The algorithms used to make the searches feasible will also be explained. The algorithms include taking advantage of some hidden structures in the nets that fold into the Nx1x1 cuboids, taking advantage of how a lot of nets fold into cuboid shapes in a 'striped' way, and using a variant of Redelmeier's algorithm. The paper ends with open questions that encourage the reader to broaden our collective understanding of the subject of creating polyomino nets.
CommentsFix Figure 3
