Why is Earth considered round despite its bumpy surface?

[rootone]

There are 2D figures and coins that are not round, but that have a constant diameter and can roll between two lines with fixed separation. In polar coordinates, the radius would be a constant term + odd harmonics.

Is there a 3D version of that? A non-spherical solid with constant diameter that fits neatly between two planes with fixed separation.

This?
https://en.wikipedia.org/wiki/Dodecahedron

 

[TeethWhitener]

The Earth has a very thin and fragile crust on a fluid mantle and a solid core. The crust floats on the surface and cannot handle tension. If you tried to roll the Earth on a flat surface it would immediately collapse, (like a fried egg), into a glob of red hot stainless steel, in the middle of a puddle of lava.

The outer core is liquid. The mantle is solid that “flows” on geologic time scales. The mantle also makes up the vast majority of the earth’s volume. This is verified readily by seismometry: the S waves radiated from earthquakes do not propagate through liquid, which would have easily observable effects of the mantle were liquid.