We will imprint your design, logo or message in any color on any shape, to make your unique air freshener.
In this sentence is "on any shape" correct or will it be "in any shape"? And what is the grammar behind the each usage?
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The grammar is identical - "in" and "on" differ only in semantics.
I would take the given sentence with "on" to mean "on an object of any shape", whereas "in" would mean "printing a area of any shape" (on something unspecified).
"In" would be much more common, so I'm guessing that the use of "on" is saying "You specify any shape, and we will cut that shape and print on it".