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In fields like geometry and numerical methods for solving differential equations we often use words like sub-face and sub-edge, referring to parts of a geometrical object. For instance, a cube has 6 faces and 12 edges. It is often necessary to refer to parts of these objects as sub-edges and sub-faces.. In the academic literature, all three forms ("sub edge", "sub-edge", and "subedge") are in use.. What would be the correct/preferred form to use?

(The word "sub-edge" cannot be found in the Oxford Dictionary, whereas "subface", can be found meaning "The undersurface of a rock formation", which is not the meaning of subface I was looking for..)

See also: Should I use hyphens with prefixes like “sub” and “semi”?

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"Sub-edge".

"Sub edge" is simply incorrect ("sub" is not its own word - at least not one you want to use in this context). It can sometimes be hard to tell (eg, "subtend" v. "sub-tend"), but when in doubt about a compound word (especially a rare or technical one), it's usually better to hyphenate.

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