TITLE: Polygons that are hard to guard
QUESTION [8 upvotes]: Given an $n$-vertex polygonal 'art gallery' $P$ in the plane, it is possible to cover the interior of $P$ by placing 'guards' at (at worst) $\lfloor n/3\rfloor$ of the vertices of $P$. That this is sufficiently many can be shown elegantly by triangulating $P$, then $3$-colouring this triangulation and placing guards at the vertices with the least common colour. 
For a lower bound only a single family of examples is needed, and the standard is the $n$-pronged comb (or crown) which has $3n$ vertices and requires one guard for each prong. However, in considering variations on the art gallery problem it can be the case that the comb is easier to guard, and thus other families (which are harder in this new context) are required. So, is there (or can we construct in comments) a big list of 'hard to guard' polygons - that is, $n$-vertex polygons for which $\lfloor n/3 \rfloor$ guards are required - that could be used as starting points for considering variations?

REPLY [12 votes]: I think this will not be a "big-list" (as per your tag), because in some sense all
examples will be variations on the same
theme.  Nevertheless, here is my offering:
     
Let $x$ be a spike tip, and $V(x)$ the set of points that see $x$.
Notice these $V(x)$ regions are disjoint for the 8 spike tips.
Therefore each tip requires its own guard, and so this shape requires $n/3$ guards.
Addendum. Now that I see Gray's motivation, it may not be inappropriate to mention
that these saw-tooth-like polygons achieve the current best lowerbounds on the transmitter problem
he mentions, as I described in "Computational Geometry Column 52" (Fig. 2).