On $2n+4$ normals conjecture for convex polytopes in ${\mathbb{R}}^n$

We prove that for $n>3$ each generic simple polytope in ${\mathbb{R}}^n$ contains a point with at least $2n+4$ emanating normals to the boundary. This result is a piecewise-linear counterpart of a long-standing problem about normals to smooth convex bodies.