N-Ta-Gon Has a Problem

N-ta-gon is a regular convex polygon shaped stadium where the polygon has N arms. Recently an alien spaceship has landed inside the stadium which is also a convex polygon but not necessarily a regular polygon. This alien ship has a weird behaviour. It needs to spin once a day within the minimum area possible to keep things functional.

This is a companion discussion topic for the original entry at https://toph.co/p/n-ta-gon-has-a-problem