1) Anglican vestment 2) Catholic clerical clothing 3) Church hat 4) Clerical cap 5) Stiff clerical cap 6) Stiff square cap 7) Worn by Roman Catholic clergy 1) Canonicals 
The biretta (biretum, birretum) is a square cap with three or four peaks or horns, sometimes surmounted by a tuft. Traditionally the three peaked biretta is worn by Roman Catholic clergy and some Anglican and Lutheran clergy. The four peaked biretta is worn as academic dress by those holding a doctoral degree from a pontifical faculty or pontifica...
square three-ridged cap worn by Catholic clergy
• (n.) Same as Berretta.
stiff square hat with three or four rounded ridges, worn by Roman Catholic, some Anglican, and some European Lutheran clergy for both liturgical and ... [1 related articles]
Square cap worn by clergy the crown has three or four projections.
Bi·ret'ta noun Same as Berretta . 
A biretta (also known as a birretta or beretta) is an ecclesiastical cap of a square shape with stiff sides and a tassel at the top. It is usually black for priests, violet for bishops and scarlet for cardinals.
[n] - a stiff cap with ridges across the crown
berretta noun a stiff cap with ridges across the crown; worn by Roman Catholic clergy
a stiff square cap with three or four upright projecting pieces extending from the center of the top to the edge, worn by ecclesiastics.