Geodesic
Rupert Properties of Polyhedra and the Generalised Nieuwland Constant
Journal for geometry and graphics, Tome 23 (2019) no. 1, pp. 29-35.

Voir la notice de l'article provenant de la source Heldermann Verlag

New results are discussed in terms of the Rupert property of polyhedra, which is about finding a hole (a straight tunnel) in a solid through which a congruent copy of the solid can pass. Recently it was proved that 8 of the 13 Archimedean solids have this property. In our paper we prove that the simplest Archimedean solid, the truncated tetrahedron is also of Rupert property. Moreover, we prove general results on the Nieuwland constant, a scaling factor between the passing and the original solids if a larger copy can also pass through. We also define a generalised Nieuwland constant for those solids not possessing this property and prove that this constant can be arbitrary small.
Classification : 51M20, 52B10
Mots-clés : Rupert property, Archimedean solids, Nieuwland constant 
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B. Hoffmann . Rupert Properties of Polyhedra and the Generalised Nieuwland Constant. Journal for geometry and graphics, Tome 23 (2019) no. 1, pp. 29-35. http://geodesic.mathdoc.fr/item/JGG_2019_23_1_JGG_2019_23_1_a2/