What is a nun's hat called?

The basic piece of a nun's hat is called a coif, but a nun's headpiece is made of several parts. The coif is a form-fitting skull cap that may be secured under the chin like a bonnet.

Several separate pieces connect to the coif and make up the nun's traditional headpiece. The band across the forehead worn under the coif is known as the bandeau. The veil is the flowing fabric that drapes from the coif down the nun's back. The wimple is the small piece that covers the neck and upper chest. The entire nun's costume, from headpiece to tunic, is known as a habit.