This hat is a Zucchetto worn by the Pope and other clerics of various Catholic Churches although I think the pope wears a white one but apparently he can wear any colour he wants.
Also worn by the higher clergy in Anglicanism, and some other Christian Orthodox churches.
Basically a small skull cap,
Zucchetto mean small gourd in Italian, this may be because the panels are sewn together to make a shape like the dome of a pumpkin or gourd.
Rabbis of Jewish faith also wear these although theirs are called kippot which is the Hebrew word for skullcap. They can also be called yarmulkes (pronounced yamakas), which is a Yiddish word taken from the Polish word also for skullcap.
Apparently the Zuchetto came in to being to keep shaven heads warm when it was the tradition for religious clerics to shave their heads. On the other hand Jews wear them as respect to God, which comes the religious book, the Talmud, which orders them to: "Cover your head in order that the fear of heaven may be upon you."
This hat is also known by the names pilus, pilos, pileus, pileolus, subbiretum, submitrale, soli deo, berrettino, calotte.
This hat is part our crew kit