The white stroke can be created by either using the rotate tool or the transform command. In either case, the degrees for rotation is determined by dividing the number of strokes by 360 degrees. The rotate tool, you can do a duplicate command to repeat the rotation, make sure your rotating a copy not the original.
Then it is up to you if you want the color of the stroke to match that of the background, or use the path finder tools to cut the paths making individual piece of the wheel. This can be handy if you would like to move a piece of the wheel outward and perhaps scale it up to draw attention to it.
