Mark Gritter<p>"Unfolding Boxes with Local Constraints" by Long Qian, Eric Wang, Bernardo Subercaseaux, and Marijn J. H. Heule <a href="https://arxiv.org/abs/2506.01079" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2506.01079</span><span class="invisible"></span></a></p><p>"We consider the problem of finding and enumerating polyominos that can be folded into multiple non-isomorphic boxes. ... In this work, we propose a new SAT-based approach that replaces these global constraints with simple local constraints that have substantially better propagation properties. Our approach dramatically improves the scalability of both computing and enumerating common box unfoldings: (i) while previous approaches could only find common unfoldings of two boxes up to area 88, ours easily scales beyond 150, and (ii) while previous approaches were only able to enumerate common unfoldings up to area 30, ours scales up to 60. This allows us to rule out 46, 54, and 58 as the smallest areas allowing a common unfolding of three boxes, thereby refuting a conjecture of Xu et al. (2017)"</p><p>Source code available, I was able to run it and find an example of a common mesh for 11x1x1 and 5x3x1 in a couple minutes. Very impressive!</p><p><a href="https://github.com/LongQianQL/CADE30-BoxUnfoldings" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">github.com/LongQianQL/CADE30-B</span><span class="invisible">oxUnfoldings</span></a></p><p><a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mathstodon.xyz/tags/folding" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>folding</span></a></p>