I recently learned of the wobbly table theorem, I won't explain it here but Numberphile has a great video on it.
But if one were to expand it could it be possible to have a stable table with n number of legs after just rotating it?
I believe at some point you couldn't because the number of legs would be so large it would just form a hollow cube without one face and regard less of how you rotate it, it would remain unstable.