What's the noun for quire? Here's the word you're looking for.
quire
One-twentieth of a ream of paper; a collection of twenty-four or twenty-five sheets of paper of the same size and quality, unfolded or having a single fold.
(bookbinding) A set of leaves which are stitched together, originally a set of four pieces of paper (eight leaves, sixteen pages). This is most often a single signature (i.e. group of four), but may be several nested signatures.
