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The phrase "assume the shape" is correct and usable in written English
It can be used when describing how something takes on a particular form or appearance. Example: "As the clay was molded, it began to assume the shape of a beautiful vase."
Exact(29)
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(31)
— 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.
The half above water assumed the shape of a goat while the lower half, the tail, assumed the shape of a fish.
Volume was approximated assuming the shape of an ellipse: (4/3) × (a × b × c).
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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