Etymology
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sedan (n.)

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.

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tetrahedron (n.)
"triangular pyramid, solid figure contained by four triangular surfaces," 1560s, from Late Greek tetraedron, noun use of neuter of tetraedros (adj.) "four-sided," from tetra- "four" (from PIE root *kwetwer- "four") + hedra "seat, base, chair, face of a geometric solid," from PIE root *sed- (1) "to sit." Related: Tetrahedral.
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Windsor 
town in Berkshire, Old English Windlesoran (c.1060), literally "bank or slope with a windlass" (Old English *windels). Site of a royal residence, hence Windsor chair (1724), Windsor tie (1895), Windsor knot in a necktie (1953).
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fallback 
also fall-back, as a noun, "a reserve," 1851, from verbal phrase, from fall (v.) + back (adv.), which is attested in the sense of "retreat" from c. 1600. As an adjective, from 1767 as a type of chair; 1930 as "that may be used in an emergency."
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polyhedron (n.)

"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").

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go-cart (n.)
also gocart, 1670s, originally "a litter, sedan chair;" also "an infant's walker" (1680s), from go + cart (n.). Later also of hand carts (1759). The modern form go-kart (1959) was coined in reference to a kind of miniature racing car with a frame body and a two-stroke engine.
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ephedra (n.)
genus of low, branchy desert shrubs, 1914, from Modern Latin (1737) from Greek ephedra, a name given by Pliny to the horsetail, literally "sitting upon," from fem. of ephedros "sitting or seated upon; sitting at or near," from epi "on" (see epi-) + hedra "seat, base, chair; face of a geometric solid," from PIE root *sed- (1) "to sit." The reason for the name is not known.
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icosahedron (n.)
"twenty-sided body," 1560s, from Latinized form of Greek eikosahedron, noun use of neuter of eikosahedros, from eikosi "twenty" + -hedra "seat, base, chair, face of a geometric solid," from PIE root *sed- (1) "to sit." Greek eikosi is from PIE *wikmti- "twenty," from *wi- "in half" (hence "two") + (d)kmti-, from root *dekm- "ten" (from PIE root *dekm- "ten"). Related: icosahedral.
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anti-macassar (n.)
also antimacassar, 1848, from anti- + macassar oil, supposedly imported from the district of Macassar on the Indonesian island of Sulawesi, which was commercially advertised from 1809 as a men's hair tonic "infallible in promoting an abundant growth and in maintaining the early hue and lustre of the HAIR to the extent of human life" [1830]. The cloth was laid to protect chair and sofa fabric from men leaning their oily heads back against it.
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settle (n.)
"long bench," 1550s, from Middle English setle "a seat," from Old English setl "a seat, stall; position, abode; setting of a heavenly body," related to sittan "to sit," from Proto-Germanic *setla- (source also of Middle Low German, Middle Dutch setel, Dutch zetel, German Sessel, Gothic sitls), from PIE *sedla- (source also of Latin sella "seat, chair," Old Church Slavonic sedlo "saddle," Old English sadol "saddle"), from root *sed- (1) "to sit."
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