Not sure about a name, but "an infinite surface with zero curvature" is an equivalent phrase.
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A plane intersects a line at a point, and i plane intersects another plane at a line.
Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few
No because in Geometry, a plane goes on infinitely. No because in Geometry, a plane goes on infinitely.
Geometry that is not on a plane, like spherical geometry
Plane Geometry and Solid Geometry