Short answers, pulled from the story.
A quarto is a book format in which the original printed sheet is folded in half twice, at right angles, producing four leaves and eight pages. The word comes from the Latin quartus, meaning fourth, because each leaf is one quarter the size of the original sheet.
A folio is made by folding a sheet once to produce two leaves and four pages. A quarto folds the sheet twice to produce four leaves and eight pages. An octavo folds the sheet three times to produce eight leaves and sixteen pages, making it smaller than the quarto when the same size paper is used.
The smallest book is Teeny Ted from Turnip Town, which measures 0.07 by 0.10 millimeters (70 micrometres by 100 micrometres). It is carved on a pure crystalline silicon page using an ion beam at Simon Fraser University in Canada.
According to the 2012 Guinness World Records, the largest book in the world was This the Prophet Mohamed, made in Dubai, UAE, measuring 5 by 8.06 meters. It holds a separate record from The Little Prince because it was not published.
The Codex Gigas, also known as the Devil's Manuscript, is the largest surviving medieval manuscript. It measures 920 by 500 millimeters.
Modern books are commonly called folio, quarto, or octavo based simply on their physical dimensions, not on how the paper was actually folded during production. Because modern printing technology uses very large sheets and perfect binding severs the link between gathering size and format, the original technical meaning of these terms no longer applies to most contemporary books.