Journal for Geometry and Graphics 23 (2019), No. 1, 029--035
Copyright Heldermann Verlag 2019
Rupert Properties of Polyhedra and the Generalised Nieuwland Constant
Dobó István High School, Széchenyi str. 19, 3300 Eger, Hungary
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.
Keywords: Rupert property, Archimedean solids, Nieuwland constant.
MSC: 51M20; 52B10
[ Fulltext-pdf (412 KB)]