A convex polyhedron without Rupert's property

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.

Publication Details

Journal
ArXiv.org
Published
2025-08-25
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

A convex polyhedron without Rupert's property

ArXiv.org
Geochemistry and Geologic Mapping
article

A convex polyhedron without Rupert's property

article en

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.

ArXiv.org
Openalex Percentile: Top 61%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
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A convex polyhedron without Rupert's property · ArXiv.org (2025) | TGRS Research Map | TGRS