By the twentieth century, the term cocked hat had come to be used more often than not in official UK usage (uniform regulations etc.) with reference to this shape of hat (particularly when worn as part of a uniform); however, in the rare instances where hats were directed to be worn side-to-side ('athwarts') rather than front-to-back—e.g. by footmen in full state livery—the term bicorn tended to be preferred.
In its most commonly seen form at this time, the cocked hat was pinned up at two sides to form a hump-back bridge shape and was worn perpendicular to the shoulders, with the front end above the face and the back end over the nape. A cockade in the national colours might be worn at the right side (French tradition) and a plume might be attached to the top (British military c. 1800). Cocked hats were often trimmed with gold or silver bullion lace and tassels. Naval officers wore them without further decorations, but those worn by military and civilian officials might be lavishly decorated with coloured ostrich or swan feathers.
So with that Bonypart pushes up his cocked hat, and begins scratching his head, and thinking and considherin’ for the bare life, and at last says he to the gineral:
“Gineral Commandher iv all the Foorces,” says he, “I’ve hot it,” says he:
Humours of Irish Life: Joseph Sheridan Le Fanu. Billy Malowney's Taste of Love and Glory
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The cocked hat (called a “three-cornered” hat, but which by Alexander’s time had in fact become a cocked hat with two peaks) was worn according to circumstances either with the peaks fore and aft or, as on this occasion, turned sideways.— A.M.
Leo Tolstoy. War and Peace
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A good-hearted old Irish nurse (whom I shall not forget in my will) took me up one day by the heels, when I was making more noise than was necessary, and swinging me round two or knocked my head into a cocked hat against the bedpost.
Edgar Allan Poe. The Works of Edgar Allan Poe — Volume 4: The Business Man (1840)
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‘If I was ever to be a lady, I’d give him a sky-blue coat with diamond buttons, nankeen trousers, a red velvet waistcoat, a cocked hat, a large gold watch, a silver pipe, and a box of money.’