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The direction of cardboard
Bend the cardboard in both directions to feel which one offers the least resistance: It bends in the direction of the fibers. So to cut a rounded box, cut it in the direction of the fibers.
On the other hand, if you are making a large box that needs rigidity, cut the outer cardboard in the opposite direction of the fibers. Then inside, on the contrary, cut it in the direction of the fibers, so you will counteract the forces.
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