There are two regular polygons: one with X sides and one with Y sides with Y>X. Also, coincidentally, the latter has internal angles that are each (Y-X) degrees greater than the former. Also, X+Y is a perfect square.
It's half past nine (local time here) as I post, so in a double handful of minutes the answer should appear -- I see it coming, with no unigons in sight (pace NS1513).
Half past Nine in the AM and then some
