For sure it couldn't work with a diamond shaped table. A diamond table would have two pairs of legs at the same radii on opposite sides of the center. Imagine

For sure it couldn't work with a diamond shaped table. A diamond table would have two pairs of legs at the same radii on opposite sides of the center. Imagine the floor is bowl shaped radially symmetrically around the center of the table. The pair of legs on a longer radius always stand on a higher part of the floor as the table spins. If the table is tipped so the top is level, both of the shorter legs are above a lower part of the floor. Tipping one short leg down to the floor tips the other one up: it is wobbly. Since everything is radially symmetric spinning the table makes no difference.