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The phrase "plane of" is correct and usable in written English.
It refers to a flat surface, often of a geometrical figure. For example, "The triangle has three equal sides and three equal angles that form a plane of symmetry."
Exact(58)
It's the plane of the decade.
– set against a plane of bright yellow.
It occupies...a plane of its own..
/ Perpendicular to the plane of the horizon.
It (wrongly) forced down the plane of Bolivia's president.
It raises them to a plane of imagined grandeur.
The tenth plane of the day roars past.
Rhabdoms are capable of resolving wavelength and plane of polarization.
In effect, the plane of the pendulum's oscillation rotates freely.
Or, at least, not in the Shockers' plane of sight.
e Gradient depth plane of background.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com