1630s, "a covered chair on poles, serving as a vehicle for one person," a word of uncertain origin, possibly from a southern Italian dialect derivative of Italian sede "chair" (compare Italian seggietta, 1590s; the thing itself was said to have originated in Naples), which is from Latin sedes, a noun related to sedere "to sit" (from PIE root *sed- (1) "to sit").
Since the date of Johnson's conjecture, however, the word has been often derived from the name of the town of Sedan in France, where it was said to have been made or first used, but historical evidence for this connection is lacking and OED frowns on it.
The thing was introduced in England by Sir Sanders Duncombe in 1634 and first called a covered chair. "In Paris the sedan-chair man was usually an Auvergnat, in London an Irishman" ["Encyclopaedia Britannica," 1929].
Brit. 'Sfoot where's my wife then?
Sam. If your wife be the gentlewoman o' the house sir, shee's now gone forth in one o' the new Hand-litters : what call yee it, a Sedan.
[Richard Brome, "The Sparagus Garden: A Comedie," 1635]
[T]heir use was greatly extended in the eighteenth century, when they were the common means of transportation for ladies and gentlemen in the cities of England and France. They were often elaborately decorated, with paintings by artists of note, panels of vernis Martin, and the like, and lined with elegant silks. Similar chairs, carried on the shoulders of two or more bearers, have long been in use in China. [Century Dictionary]
Meaning "closed automobile seating four or more" is recorded by 1911, American English, in automotive journals. Middle English had sede (n.) "a chair, seat" (early 14c.), from Latin sedes.
"a solid bounded by many (usually more than 6) plane faces," 1560s, from Latinized form of Greek polyedron, neuter of adjective polyedros "having many bases or sides," from polys "many" (from PIE root *pele- (1) "to fill") + hedra "seat, base, chair, face of a geometric solid" (from PIE root *sed- (1) "to sit").