This is well-worn Kufi style cap I got as part of a eBay hat bid last year.
This cap has a colourful brim folded up only around 2/3rds of its diameter making it unusual.
I happy to wear it back to front as the above image, it works either way in my opinion.
When I took these photos I did not realise one side of the turn-up brim was distorted, a quick iron or stitch will fix this.
Looking at the hat know I'm wondering what the hat would look like with its folded up section folded down.