I have two questions the same as Mostafa's Question: Visibility of vertices in polyhedra
Suppose $P$ is a closed polyhedron in space (i.e. a union of polygons which is homeomorphic to $S^2$) and $X$ is an interior point of $P$. We know that maybe $X$ can't see any entire face or edge of $P$, because in O'Rourke or Khezeli's examples $X$ can't see any vertex of $P$. But how about just part of faces or edges in $X$'s view. At least how many faces or edges can $X$ see, even part of them?
So let $X$ is a light point inside a simple polyhedron $P$:
- Is it true that $X$ can see part of at least four different faces of $P$?
- Is it true that $X$ can see part of at least six different edges of $P$?
We proved Q1, I think the answer of Q2 is Yes too, but I have no simple idea yet.