Hats particularly fedora's / cowboy hats get much of their looks from the creases and dents put in the crown.
Below are the 6 main types in my opinion
Open crown
Also called a round crown, open crowns don’t have any creases at all, basically a dome shape prior to creasing.
Centre dent
This crown shape is also called a centre crease, a shape that features a single crease down the centre of the crown
Telescope
Also called a flat crown or flat top, a telescope crown is marked by its simple circular indentation
Diamond dent
The crown is diamond-shaped when viewed from the top
Teardrop dent
This crown type can be identified by a teardrop shape that is more pointed at the front and curved at back.
Cattleman dent
This crown type has a main centre dent/crease with 2 smaller creases on either side
