  A deflated polygon is a polygon with no visibility crossings. We answer a
question posed by Devadoss et al. (2012) by presenting a polygon that cannot be
deformed via continuous visibility-decreasing motion into a deflated polygon.
We show that the least n for which there exists such an n-gon is seven. In
order to demonstrate non-deflatability, we use a new combinatorial structure
for polygons, the directed dual, which encodes the visibility properties of
deflated polygons. We also show that any two deflated polygons with the same
directed dual can be deformed, one into the other, through a
visibility-preserving deformation.
