Let's start with the conclusion that a circle rolls around a polygon. If the circumference of a polygon is n times that of a circle, then when the circle rolls to its original position, it rolls (n+ 1) times.

The number of circles that a circle finally rolls = (the distance that the center of the circle moves)/the circumference of the circle.

When scrolling on a polygon, the perimeter of the polygon is part of the scrolling distance. When scrolling to each vertex with the center of the circle, the running route is an arc. The radius of these arcs is equal to the radius of the circle, and the sum of the central angles is 360 degrees, which is the circumference of the circle.

So this question, scroll 4 times.

It may not be clear, for reference only.