Can this twisted table be built so it doesn’t collapse? (Can it exist in nature or is it such a bad design it’ll immediately collapse?)

Drawings below are done with Pov-Ray and Moray

The concept is each leg goes at a 45 degree angle so it ends up under a different corner of the table top.

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This is a lower angle view of the twisted table.

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Zooming in on one corner. How can the leg be attached solidly? This is a “surface mount” variation with no cuts made to the table top. Possible places a dowel or screw could be put in are shown.

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This looks more solid but involves a tricky cut to the table top. The leg has more “meat” to grab ahold of, and a 3rd direction for a dowel/screw is now possible.

The table cut is exaggerated, along with holes for the dowels.

With reasonable dimensions it should be possible to put in multiple dowels e.g. if the table top is 24” x 24” x 2”, and legs are 2” x 2” x 33” (approx) then there should be plenty of room in the leg for 2 or more dowels.

The key engineering question in the picture above is, which vectors for the dowels would give the most strength to deal with a downward force – the pinkish one, the green, or the yellow?