10-normals conjecture for simple convex polytopes in R^3

Prove that every simple convex polytope P contained in R^3 has an interior point y from which at least 10 normals to the boundary ∂P emanate.

Background

The authors introduce n(P, y) as the number of boundary normals from an interior point y and define N(P) as the maximum of n(P, y) over interior points. They show a general lower bound N(P) ≥ 2n + 2, which gives N(P) ≥ 8 in R^3, and then propose strengthening this for simple polytopes in dimension three.

They verify the conjecture for several classes (tetrahedra and triangular prisms) and develop sufficient conditions involving spherical geometry of vertex links, suggesting broad validity while leaving the general case open.