Rupert Property of Archimedean Solids

  title={Rupert Property of Archimedean Solids},
  author={Ying Chai and Liping Yuan and Tudor Zamfirescu},
  journal={The American Mathematical Monthly},
  pages={497 - 504}
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. 
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
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
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
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.


Platonic Passages
Summary It is well known that a hole can be cut in a cube large enough to permit a second cube of equal size to pass through, a result attributed to Prince Rupert of the Rhine by J. Wallis more than
Acute Triangulations of the Cuboctahedral Surface
It is proved that the surface of the cuboctahedron can be triangulated into 8 non-obtuse triangles and 12 acute triangles and both bounds are the best possible.
Acute Triangulations of Archimedean Surfaces . The Truncated Tetrahedron
In this paper we prove that the surface of the regular truncated tetrahedron can be triangulated into 10 non-obtuse geodesic triangles, and also into 12 acute geodesic triangles. Furthermore, we show
On the translative packing densities of tetrahedra and cubooctahedra
Universal Stoppers Are Rupert
John Wetzel earned his Ph.D. at Stanford in 1964 after undergraduate work at Purdue. His entire academic career was spent at the University of Illinois, from which he retired in
Dense packings of the Platonic and Archimedean solids
This corrects the article DOI: 10.1038/nature08239
Prince Rupert's problem and its extension by Pieter Nieuwland
  • Scripta Math
  • 1950
Das problem des Prinzen Ruprecht von der Pfalz
  • Praxis der Math
  • 1968