This pill box shaped soft hat is what you might call a smoking cap.
A very simple ring of fabric with a fabric lid, this one is not decorated, covered in sequins, buttons, embroidered or tasselled but does have colourful panels.
A very comfortable hat mainly for indoor use as it offer a bit of warmth to a balding head like mine.
Makes a excellent hat for a north African/Arabic trader character
In parts of Africa this would be called a kufi, kofi hat.
In parts of Africa this would be called a kufi, kofi hat.