A convex polyhedron without Rupert's property
2025/08/25 by Jakob Steininger, Sergey Yurkevich, Steininger, Jakob +1 · 9 voices
#math.MG #cs.CG #math.CO
paper · pdf · doi:10.48550/arxiv.2508.18475
Abstract
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.
Discussions
- The conjecture that every convex polyhedron is Rupert is settled in the negative! The convex body in the image cannot pass straight through a hole inside itself. arxiv.org/abs/2508.18475 #Mathematics [bsky, 37 points, 1 comments]
- A convex polyhedron without Rupert's property [hn, 28 points, 1 comments]
- A convex polyhedron without Rupert's property [hn, 14 points, 0 comments]
- This week Steininger and Yurkevich found this convex polyhedron that you *can't* cut a hole in that's big enough to slide the entire polyhedron through the hole. They gave it a silly name. arxiv.org/a [bsky, 4 points, 0 comments]
- Also, this is interesting, on the note of math stuff.. “A convex polyhedron without Rupert’s Property”. arxiv.org/pdf/2508.18475 [bsky, 1 points, 0 comments]
- *Wait... Prince Rupert of the Rhine is in breaking science news this week? *The* Rupert of the Rhine, the guy with the glass drops and the battle-poodle and all that? Gee whiz https://arxiv.org/pdf/25 [bsky, 1 points, 0 comments]
- They found a polyhedron that is Rupert but not locally Rupert! [bsky, 1 points, 0 comments]
- A convex polyhedron without Rupert's property https://arxiv.org/abs/2508.18475 [bsky, 0 points, 0 comments]
- this looks like some nice work, basically understandable by anyone familiar with very rudimentary real analysis and linear algebra arxiv.org/abs/2508.18475 [bsky, 0 points, 0 comments]
Related