The most common meanings of coif are a hair style and a
tightfitting cap.
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From the Old French, the verb "coif" (kwaff) means to arrange hair, as seen in the word coiffure (hairdo). The noun "coif" is a skullcap or tight-fitting cap, such as worn by nuns.
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Coif was invented approximately 100 years ago, around the same time as the hair style a bob! =D