It's well known that a three feet chair can stand correctly on any (regular enough) surface (let alone the intersection between the chair and the surface!and chairs orientation).
How about four feets chairs. I obviously found plane and sphere. I tried to find them all but wasn't able to do so.
Nb : chairs can be any size.
Any hint?
Assume the leg tips form in 3-space a square with diagonal $d$. Then there can be no third example of such a surface. This is because of rotation requirement:
A hollow cylinder of diameter $d$ and negligible thickness needs to contact ( along a tangent cone of the sphere or plane ) on the surface at its cylinder end.