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},
  url={https://api.semanticscholar.org/CorpusID:125508192}
}
It is shown that among the 13 Archimedean solids, 8 have this property, namely, the cuboctahedron, the truncated octahedrons, thetruncated cube, the rhombicuboctahedral, the icosidodecahedral, and the truncation dodecahedron.
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11 Citations
Background Citations
2
Methods Citations
1
Results Citations
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11 Citations

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8 References

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

Dense packings of the Platonic and Archimedean solids

Dense particle packings have served as useful models of the structures of liquid, glassy and crystalline states of matter, granular media, heterogeneous materials and biological systems. Probing the…

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John Wetzel [email protected]) 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…

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