This is one of those hats that falls into the category unknown, from a theatrical production, its has a Arabian Nights feel about it.
The hexagonal shape of this soft head covering is also odd, so far I've not found any images of anything similar to it.
It sits uncomfortable because of its design, resting too high on the crown of your head, but that adds to its unique look.
It also could have been for a male or female character, it seems to suit both.
