arXiv:2508.18475math.MG
A three-dimensional convex body is said to have Rupert's property if its copy can be passed through a straight hole inside that body. In this work we construct a polyhedron which is provably not Rupert, thus we disprove a conjecture from 2017. We also find a polyhedron that is Rupert but not locally Rupert.
Linked by 3 identifiable commenters in 3 comments across 3 threads, from Oct 2025 to Dec 2025. Found in 3 HN submissions from Aug 2025 to Oct 2025. Open submission discussions.
I'm working on formalizing https://arxiv.org/pdf/2508.18475 (A convex polyhedron without Rupert's property) in Lean4 I'm only on lemma 11 at this point, and up until that point the paper has been fairly easy to formalize (modulo my unfamiliarity with mathlib). The repo is here…
This was discussed on HN previously https://news.ycombinator.com/item?id=45057561 And I thought that the paper http://arxiv.org/abs/2508.18475 had also been discussed but can’t find it so could be wrong
https://arxiv.org/abs/2508.18475 Rupert's snub cube and other Math Holes - https://news.ycombinator.com/item?id=45261566 - Sept 2025 (10 comments) Rupert's Property - https://news.ycombinator.com/item?id=45057561 - Aug 2025 (23 comments)
Connected through shared HN threads, not inferred similarity or a recommendation.
this video is new and an easy watch, based on this paper which has been on here before https://arxiv.org/pdf/2508.18475 and here's the Tom7 video he recommends if you want to go deeper https://www.youtube.com/watch?v=QH4MviUE0_s
fsckboyView on HNParent context