Iain M. Banks last Culture book has a "advanced civilization with more aesthetics than sanity" that had polished a moon much like a marble, that'd then been lowered down towards the planet it orbited while adjusting the orbital speed accordingly. They'd cut a trench around the entire planet, so that said moon were eventually orbiting below the surrounding planet surface.... One of the main civilizations in the book had then "inherited it" and used the moon as the headquarters of one of their military branches.

It's fun to speculate just how bizarre results you could get if you had a civilization with enough resources to do planetary scale arts projects just for the heck of it...

Wouldn't the planet's atmosphere and oceans fall into the trench?

Yes, which is why you dig the trench deep enough to cover it over again, make it airtight, and pump out all of the atmosphere to make a vacuum torus inside the planet.

There were either walls on either side of the trench, or the planet was a barren rock to begin with.

Of course. An advanced civilization with engineering sense wouldn't waste precious building materials on thousands of kilometers of planetary bedrock.

(And that's to say nothing of that area/volume ratio, what that implies for radiative heat rejection!)

And a termite might think that an advanced civilization would never spend tons of valuable vegetable matter for purely aesthetic reasons.

It's all about the relative abilities. It's not completely unconcievable that some might transform planets the way we build funny houses, even if they are 'waste of precious building materials'.

I seem to recall that the Culture does regard planets as being rather wasteful of mass - much more efficient to build an O.

NB I'm sure some Culture ships have probably built planets in idle moments - just for the hell of it.

“Welcome to Magrathea, where we construct planets made to order.” (Source: The Hitchhiker’s Guide to the Galaxy)