A square cap with three peaks or ridges on top. A pompon in the center usually ornaments it. By the Middle Ages, the hood of the cope was rarely worn because it had become tight-fitting and richly ornamented. Some other protection from the cold was necessary for the head of the tonsured cleric. A skullcap was used, but more often a cap of soft material was worn with a tuft on top by which it could be removed easily. This cap was known as a pileus or birettum. By the 16th century, the birettum was reinforced with an interlining of stiff canvas to give it a neat appearance. The mortarboard used in academic dress seems to be a flattened birettum and a skullcap combined.
Bibliography: a. a. king, Liturgy of the Roman Church (Milwaukee 1957). h. norris, Church Vestments: Their Origin and Development (New York 1950).
"Biretta." New Catholic Encyclopedia. . Encyclopedia.com. (August 19, 2018). http://www.encyclopedia.com/religion/encyclopedias-almanacs-transcripts-and-maps/biretta
"Biretta." New Catholic Encyclopedia. . Retrieved August 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/religion/encyclopedias-almanacs-transcripts-and-maps/biretta