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The phrase "all three dimensions" is correct and usable in written English.
You can use it when referring to three distinct aspects or dimensions of a particular subject or concept.
Example: "In our analysis, we need to consider all three dimensions: economic, social, and environmental."
Alternatives: "the three aspects" or "all three facets".
Exact(60)
Provides instantaneous feedback for physical movement in all three dimensions.
Such crystals can extend indefinitely in all three dimensions.
This is realized for crystals in all three dimensions.
Poetry seems to involve all three dimensions of time: past, present and future.
When that failed, they decided to try comparing carabiners along all three dimensions at once.
But when you look at all three dimensions, the big suppliers actually do quite poorly.
Sophisticated negotiators act in all three dimensions to create and claim value.
But in the magnetic state, ordering occurs between neighboring electron pairs in all three dimensions.
Finally, electrons can be confined in all three dimensions in a "quantum dot" or "artificial atom".
7. Provides instantaneous feedback for physical movement in all three dimensions.
Sustainability in all three dimensions, economy, environment, and society, is increasingly relevant in engineering.
More suggestions(16)
all three constraints
all three observations
all three phenomena
all three spheres
all three perspectives
all three determinants
all three consequences
all three criteria
all three conditions
all three sizes
all three disciplines
all three implications
all three classifications
all three questions
all three issues
all three sections
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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