I was informed when I purchase this hat that it was Pannonian Pileus, not sure how true this is, however looking for info to check this out Pannonian hats do appear to be this shape, although the ones I've seen seem to be made of fur or skin rather than felt, so is at the very least not far from the truth.
The traditional Pileus Hat is a brimless cone (not like this hat) of felt worn by Greek Roman sailors from around 375 B.C. to the 4th century A.D.
