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The phrase "assume the shape of" is correct and can be used in written English
It is used to talk about something taking on the form of something else. For example: The liquid slowly assumed the shape of the container it was poured into.
Exact(24)
Strip by strip, the board began to assume the shape of a gentle arch.
I mean, would God really let the Devil assume the shape of an innocent?
This winning combination of mechanical properties allows it to assume the shape of any object through creasing and folding.
Traditional theories fail to fit data, probably for because they assume the shape of the electric field.
There may be interesting and moving experiences, but one thing is guaranteed: they won't naturally assume the shape of a wonderful book".
Embedded in these asides is the story of Austerlitz himself, whose ongoing conversations with the book's nameless narrator slowly assume the shape of an autobiography.
Similar(36)
To David Reynard, the shape and size of Susan's tumor — a hazy line swerving from the left side of her midbrain to the hindbrain — uncannily resembled a malignant shadow of the phone (but tumors, like clouds, can assume the shapes of our imaginations).
— capable of assuming the shape of motor vehicles.
She set the fur down on the pavement where it assumed the shape of a dog.
Day Two integrates itself into the BBC1 schedule by assuming the shape of a Spooks episode.
Volume was approximated assuming the shape of an ellipse: (4/3) × (a × b × c).
More suggestions(20)
play the shape of
think the shape of
understand the shape of
take the shape of
imagine the shape of
anticipate the shape of
conclude the shape of
suggest the shape of
deduce the shape of
consider the shape of
adopt the shape of
bear the shape of
guess the shape of
expect the shape of
infer the shape of
assume the position of
assume the nature of
assume the sale of
assume the Mastership of
assume the burden of
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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