Well that all depends on what you are asking about because "a plane" can be:
A flat level surface
A level of existence
A flying vehicle (short for aeroplane)
A carpenters tool
A trowel
A species of tree
A wing
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The coordinate plane is sometimes call the Cartesian plane because Rene Descartes is often credited with inventing the coordinate plane and so the coordinate plane is sometimes called the Cartesian plane,in his honor.
You can call it anything you like.
An octagon.
A decagon.
A dodecagon.