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The phrase "across three dimensions" is correct and usable in written English.
It can be used when discussing concepts or phenomena that involve multiple dimensions, such as in physics, mathematics, or design.
Example: "The artist's work explores the interaction of light and shadow across three dimensions, creating a captivating visual experience."
Alternatives: "in three dimensions" or "through three dimensions".
Exact(26)
Paul Michelman: So, we're going to look at this question across three dimensions.
Yet scanless measurement of the high-speed activity of individual neurons across three dimensions in scattering mammalian tissue remains an open problem.
Then, using the coverage-box framework, we assess their progress across three dimensions of coverage: who, what services, and what proportion of health costs are covered.
At its root, the reason MBA programs fail to produce better thinkers is structural, and it runs across three dimensions: where the curriculum's content should be deep, it is shallow; where it should be broad, it is narrow; and where it should be dynamic, it is static.
CTM-driven innovation and development has the potential to achieve step-change improvements across three dimensions.
The potential for exploiting signal sparsity across three dimensions, namely time, frequency, and channels, is analyzed.
Similar(34)
The diversity of this sales ops role cuts across two dimensions.
The labs work to understand health across four dimensions: aging, emotion, relationships, and race and social class.
The chart below compares Britain's economic performance to that of other big OECD countries across four dimensions: GDP growth, inflation, budget balance and unemployment.
The OSI-R model is theory-based and assesses the effects on the individual of three 'factors' (occupational roles, psychological strain, and coping resources) across fourteen dimensions.
We then develop a scale to assess the strength of linkage across five dimensions: species, habitat, spatial, temporal and conservation association.
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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