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arXiv · 2508.18475

A convex polyhedron without Rupert's property

Jakob Steininger·Sergey Yurkevich
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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.

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Jakob Steininger, Sergey Yurkevich. 2026-01-28. A convex polyhedron without Rupert's property. https://arxiv.org/abs/2508.18475

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