Minimizing Visible Edges in Polyhedra

We prove that, given a polyhedron 𝒫 in ℝ^3 , every point in ℝ^3 that does not see any vertex of 𝒫 must see eight or more edges of 𝒫 , and this bound is tight. More generally, this remains true if 𝒫 is any finite arrangement of internally disjoint polygons in ℝ^3 . We also prove that every point in ℝ^3 can see six or more edges of 𝒫 (possibly only the endpoints of some these edges) and every point in the interior of 𝒫 can see a positive portion of at least six edges of 𝒫 . These bounds are also tight.