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WordNet
campaign hat

n. a broad-brimmed felt hat with a high crown; formerly worn by the United States Army and Marine personnel

Wikipedia
Campaign hat

A campaign hat is a broad-brimmed felt or straw hat, with a high crown, pinched symmetrically at the four corners (the "Montana crease").

The hat is most commonly worn as part of a uniform; it is worn by such agencies as the New Zealand Army, the Royal Canadian Mounted Police, United States park rangers, and Boy Scouts.

Although the campaign hat is occasionally referred to as a Stetson, this is from its common manufacture in the late 19th century by that company. It should not be confused with the quite different Stetson hat type with a different brim and crease, commonly known as the cowboy hat, and which is more commonly meant by the term "Stetson" today. The campaign hat also should not be confused with a slouch hat.