Dodecahedron and Icosahedron Nieuwland numbers
Prove that the Dodecahedron and the Icosahedron both have Nieuwland number ν ≈ 1.0108, where ν is the root of P(x) = 2025x^8 − 11970x^6 + 17009x^4 − 9000x^2 + 2000, thereby confirming the conjectured optimal passage ratios for these Platonic solids.
References
It is, for instance, still open to prove that the Octahedron has Nieuwland number 3√2/4 or that the Dodecahedron and Icosahedron both have Nieuwland number ν ≈ 1.0108, a root of ( P(x) = 2025x8 - 11970x6 + 17009x4 - 9000x2 + 2000 ).
— A convex polyhedron without Rupert's property
(Steininger et al., 25 Aug 2025) in Section 9.2, Open Problems