"Chapeau de Bras", transliterated from French, means 'hat of arms'. I presume this arises from the fact that the design is collapsible and can be held under the arm, rather than that it was in origin a military hat.

The Chapeau is a Regency-era hat, and was popular among military gentlemen. The fact that the hat was collapsible also endeared it to civilians, who found it convenient to tuck the hat under one arm while attending the opera. In military form it could be flamboyantly decorated. This design has red and white ostrich plumes, a gold hatband, gold braid edging, and a red cockade. The cockade is held in place by a gold braid strap fixed by a gold button. More gold braid tumbles over the brim fore and aft. The body of the hat is black felt.

It goes without saying that this hat will work without glitching, with all my hair styles.