Jakob Steininger, Sergey Yurkevich
2025 · arXiv
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.
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3 selected excerpts · 3 total mentions
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
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 https://github.com/badly-drawn-wizards/noperthedron
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
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