French cuff
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A French cuff or double cuff (primarily British) is a cuff on a dress shirt that is closed using cuff links instead of buttons (it is a link cuff), and is twice as long as a single cuff, but worn folded back on itself.
Instead of cuff links, French cuffs can also be closed with silk knots, sometimes called monkey's fists, which are cheaper. Silk knots tend to be better known in Europe than in North America. Cuff links and silk knots exist solely for shirts with link cuffs, either double or single.
French cuffs are considered to be more formal than button cuffs, although they are seeing a resurgence in the business environment. They are generally a matter of preference with a business suit, however French cuffs are preferred for black tie.