Problem
Research questions and friction points this paper is trying to address.
polyomino nets
cuboids
surface area
Polyomino Nets Covering Three Different Boxes of Area 106 and Related Results
🤖 AI Summary
研究通过计算机搜索找到可折叠成三种不同表面积为106的长方体的40种多格骨牌网络，并利用特定算法优化搜索过程。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
polyomino nets
computer search
cuboids
surface area 106
Redelmeier's algorithm
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