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