Existence of a convex polytope in R^3 with N(P) = 8

Determine whether there exists a convex polytope P contained in R^3 such that the maximal number of normals to the boundary ∂P emanating from an interior point, N(P) = max_y n(P, y), equals 8.

Background

For polytopes in R^3, the authors prove a universal lower bound N(P) ≥ 8. They further conjecture N(P) ≥ 10 for simple polytopes and confirm this bound for tetrahedra and triangular prisms. Despite these advances, it remains unclear whether any polytope attains exactly the lower bound of 8, which would exhibit the minimal possible maximal count of normals.

This question is central to distinguishing whether the stronger 10-normals behavior is ubiquitous or whether some polytopes achieve only the minimal bound ensured by general arguments.