# Rupert Property of Archimedean Solids

```@article{Chai2018RupertPO,
title={Rupert Property of Archimedean Solids},
author={Ying Chai and Liping Yuan and Tudor Zamfirescu},
journal={The American Mathematical Monthly},
year={2018},
volume={125},
pages={497 - 504}
}```
• Published 24 May 2018
• Mathematics
• The American Mathematical Monthly
Abstract We say that a polytope has the Rupert property if we can make a hole large enough in to permit another copy of to pass through. In this article, we show that among the 13 Archimedean solids, 8 have this property, namely, the cuboctahedron, the truncated octahedron, the truncated cube, the rhombicuboctahedron, the icosidodecahedron, the truncated cuboctahedron, the truncated icosahedron, and the truncated dodecahedron.
5 Citations
The Truncated Tetrahedron Is Rupert
Abstract A polyhedron has the Rupert property if a straight tunnel can be made in it, large enough so that a copy of can pass through this tunnel. Eight Archimedean polyhedra are known to have the
An algorithmic approach to Rupert's problem
• Mathematics
• 2021
A polyhedron P ⊂ R has Rupert’s property if a hole can be cut into it, such that a copy of P can pass through this hole. There are several works investigating this property for some specific
The n-Cube is Rupert
• Physics, Economics
Am. Math. Mon.
• 2018
It is shown that the n-cube is Rupert for each n ⩾ 3, because a straight tunnel can be made in it through which a second congruent oval can be passed.
Cubes and Boxes Have Rupert’s Passages in Every Nontrivial Direction
• Mathematics
Am. Math. Mon.
• 2021
It is proved that cubes and, in fact all, rectangular boxes have Rupert's passages in every direction that is not parallel to the faces, not only for the cube, but also for all other rectangular boxes.

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