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The Collaborative International Dictionary
Faying surface

Fay \Fay\, v. i. (Shipbuilding) To lie close together; to fit; to fadge; -- often with in, into, with, or together.

Faying surface, that surface of an object which comes with another object to which it is fastened; -- said of plates, angle irons, etc., that are riveted together in shipwork.

Wiktionary
faying surface

n. Either of a pair of surfaces that are in contact in a joint.

Wikipedia
Faying surface

A faying surface is one of the surfaces that are in contact at a joint.

Faying surfaces may be connected to each other by bolts or rivets, or by adhesives or welding. An example would be steel pipe flanges.