Compond Mitre for top lid.skp (57.7 KB)
See the attached.
If you want to show the segments ans individual parts, make a single part as a component. In this case, make one segment and use Copy/Rotate to make the rest.
In step two you can open one instance of the segment component and use Intersect Faces or you might find it easier to understand what’s getting cut if you use the Line tool to trace where the faces pass through the neighbor. I placed only two instances of the component in hopes it would be clearer what’s going on. In practice, I would go ahead and make all the required copies from the beginning. Then I would open one instance of the component for editing and trace where its neighbors intersect on both sides.
After those lines are drawn, erase the waste sides of the lines.