  We explicitly compute the limiting slope gap distribution for saddle
connections on any 2n-gon. Our calculations show that the slope gap
distribution for a translation surface is not always unimodal, answering a
question of Athreya. We also give linear lower and upper bounds for number of
non-differentiability points as n grows. The latter result exhibits the first
example of a non-trivial bound on an infinite family of translation surfaces
and answers a question by Kumanduri-Sanchez-Wang.
