Cube in space with water around it

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Consider an Earth-sized cube in space and surround it with enough water that gravity causes the water to just touch the corners of the cube, what shape will the water form?

I suspect it won't be entirely circular but cannot justify my thoughts.

2D guess

I suspect the shape will approach a cube and look more like $x^4 + y^4 + z^4 = r^4$

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This research paper will help you imagine https://thescipub.com/PDF/pisp.2012.50.57.pdf