A plane.
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It is a polyhedron.
A flat surface with two dimensional shape.
The surface area pf the Earth is on a sphere, not a flat surface.
A plane is a flat, two-dimensional surface that extends infinitely far
You can't. Not in this universe, anyway. The problem in reverse has challenged cartographers for centuries. How do you map a global earth onto a flat surface? There are many different "projections" that represent various compromises and characteristics, but no two-dimensional representation can completely capture the unique nature of a globe.