My safari hat is a modern rendition of the Giggle Hat, otherwise known in military speak as Hats, Rags, Rediculous. Also a Barmah Squashy hat. It is made of thin Kangaroo leather.

Like John said both these have the top of the hat sitting on the top of your head. Still use and prefer the old Sloutch hat in hot open places.

My Hats rags rediculous.