Can there be a 100% rigid object i.e., an object that cannot be compresses any bit? I believe that's not possible. The proof below- Suppose there is one such object(cubic shaped). I have applied a force on that from two opposite or all six sides. From newton's third law the object is also applying back a force. Suppose we seal the object from all the sides in the same state(i.e., the forces are still acting there). Now take another identical object and seal that easily without wrestling much with that. Now observe the two sealed boxes. If the object is incompressible then there would be absolutely no difference between the two sealed boxes. But in the first case forces are acting against the walls of the box and in the second case there are no or little forces acting between the object and the wall which means cases are not identical. Thus we arrive at a place of contradiction. Therefore there must be some compression that would distinguish the first from the second. Hence, 100% incompressible object is theoretically not possible. However I acknowledge that compression may be as little as one would want. That however little compression would result in the opposite force, compression given by, L= F/k. But 0% compression is not possible.