Question 135
Call a convex polygon on a plane *correct* if for its every side there exists a unique vertex of the polygon that lies farther from that side than any other vertex of the polygon. Call the perpendicular drawn from the vertex farthest from side $XY$ to side $XY$ an *altitude* of the correct polygon. Find all natural numbers $n$ for which there exists a correct $n$-gon whose all $n$ altitudes meet in one point.