The Japanese Kumiko geometry is well known for its repetitive patterns with fractalic appearance. The small masses, placed in a repetitive pattern, produce gravitational distortions in spacetime. Being identical objects in pattern, when the frequency of the initial object's vibration matches the resonant frequency or natural frequency of the second object and so on, a resonant behavior occurs and the local extended deformation in the nearby spacetime produces a vectorial micro-gravitational field.
This vectorial field can be created and placed against the Earth's gravity - and when this happens, the object would simply fly. 

To prevent the upward displacement of the flying table, three equidistant strings are connected between the flying part and an added base. A fourth string should be centrally connected to complete the connection pattern.
For safety reasons please do not scale up or print larger / heavier flying tables. 

 

I hope the above statements did not puzzle you too much. While most of the statements are correct, the conclusion is forced and incorrect - the Earth's gravitational force would still work as usual. The fourth central connection is what keeps the table "flying".

I have seen a few other constructions on the same idea - but all very difficult to be set in the “flying” position. A small tooling device greatly helps to keep everything in place until the string connections are made. Mount both sides of the table in the tooling and add string links as in the schematic. Put just a light tension in each of these strings. Carefully remove the tooling when all the string connections are made - done!

I have used very thick Ø1mm nylon string and it is clearly visible in the close-by pictures - but 0,3mm-0,4mm fishing string would improve the visual flying illusion. And of course the models can be scaled :) I did myself a scaled XYZ 138/138/200 % that can be seen in some pictures.