A convex polyhedron without Rupert's property
Metric Geometry
2026-01-30 v2 Computational Geometry
Combinatorics
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.
Cite
@article{arxiv.2508.18475,
title = {A convex polyhedron without Rupert's property},
author = {Jakob Steininger and Sergey Yurkevich},
journal= {arXiv preprint arXiv:2508.18475},
year = {2026}
}