Crown: the part of the hat that covers the top of your head
Bash, crease: the indent and shape of the indent of the top of the crown, or lack of (flat)
Dent, pinch: indentations on the front and sides of the crown
Crown wall, sidewall: the side of the crown from the break to to top of the crown
Break: where the crown and the brim joins
Brim: the horizontal part of the hat that extends from the bottom of the crown
Brim edge: the edge of the brim refers to how the brim is finished
Dip: the slope of the brim overall from the break, or the front or back portion of the brim
Band: the decorative and functional belt around the crown just above the break
Sweatband, inner band: band inside the crown for moisture control or cushioning
Underbrim: the underside of the brim
Lining: the lining of the inside of the crown