Etymology
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polysymmetrical (adj.)

"divisible into exactly similar halves by more than one plane," by 1875; see poly- "many" + symmetrical. Related: Polysymmetry; polysymmetrically.

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raphe (n.)

in anatomy, "seam-like suture of two lateral halves," 1753, medical Latin, from Greek rhaphē "seam, suture (of a skull)," from rhaptein "to sew together, stitch" (from PIE root *wer- (2) "to turn, bend").

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valve (n.)
late 14c., "one of the halves of a folding door," from Latin valva (plural valvae) "section of a folding or revolving door," literally "that which turns," related to volvere "to roll," from PIE root *wel- (3) "to turn, revolve." Sense extended 1610s to "membranous fold regulating flow of bodily fluids;" 1650s to "mechanical device that works like an anatomical valve;" and 1660s in zoology to "halves of a hinged shell." Related: Valved.
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halve (v.)
Middle English halven, halfen "to divide in halves" (c. 1200), from half (n.). Meaning "to reduce by half" is from c. 1400. Related: Halved; halving.
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bellows (n.)
"instrument for producing a current of air," especially for a fire, c. 1200, belwes, literally "bags," plural of belu, belw, northern form of beli, from late Old English belg "pair of bellows; bag, purse, leathern bottle," from PIE *bhelgh- "to swell," extended form of root *bhel- (2) "to blow, swell."

Essentially the same word as belly (n.) and retaining its original sense. It is attested earlier in the specific term blæstbælg, literally "blowing bag," and the modern word is perhaps a reduction of this (compare Old Norse blastrbelgr, German Blasebalg). Used exclusively in plural since 15c., probably due to the two handles or halves.
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scarf (n.1)

[band of silk, strip of cloth], 1550s, "a band worn across the body or over the shoulders," probably from Old North French escarpe "sash, sling," which probably is identical with Old French escherpe "pilgrim's purse suspended from the neck," perhaps from Frankish *skirpja or some other Germanic source (compare Old Norse skreppa "small bag, wallet, satchel"), or from Medieval Latin scirpa "little bag woven of rushes," from Latin scirpus "rush, bulrush," which is of unknown origin [Klein].

It also is attested in early Modern English as scarp. OED points to "the change of the initial p into f after liquids". As a cold-weather covering of warm and soft material for the neck, by 1844. Plural scarfs began to yield to scarves early 18c., on model of half/halves, etc.

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tally (n.)
mid-15c., "stick marked with notches to indicate amount owed or paid," from Anglo-French tallie (early 14c., Old French taille "notch in a piece of wood signifying a debt"), Anglo-Latin talea (late 12c.), from Medieval Latin tallia, from Latin talea "a cutting, rod, stick" (see tailor (n.), and compare sense history of score). Meaning "a thing that matches another" first recorded 1650s, from practice of splitting a tally lengthwise across the notches, debtor and creditor each retaining one of the halves; the usual method of keeping accounts before writing became general (the size of the notches varied with the amount). Sports sense of "a total score" is from 1856. Also in 19c. British provincial verbal expression live tally, make a tally bargain "live as husband and wife without marrying."
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medal (n.)

1580s, "a metal disk bearing a figure or inscription," from French médaille (15c.), from Italian medaglia "a medal," according to OED from Vulgar Latin *metallea (moneta) "metal (coin)," from Latin metallum (see metal). The other theory [Klein, Barnhart, Watkins] is that medaglia originally meant "coin worth half a denarius," and is from Vulgar Latin *medalia, from Late Latin medialia "little halves," neuter plural of medialis "of the middle" (from PIE root *medhyo- "middle").

Originally in reference to a trinket or charm; by 1610s as a commemorative of a person, institution, or event. As a reward for merit, proficiency, etc., it is attested by 1751. A medal is distinguished from a coin by not being intended to serve as a medium of exchange, but in 18c. English, as in older French and Italian, it was applied to old coins no longer in circulation kept as curiosities.  Related: Medallic.

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*dhwer- 

Proto-Indo-European root meaning "door, doorway." The base form is frequently in dual or plural, leading to speculation that houses of the original Indo-Europeans had doors with two swinging halves.

It forms all or part of: afforest; deforest; door; faubourg; foreclose; foreign; forensic; forest; forfeit; forum; hors d'oeuvre; thyroid.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit duárah "door, gate;" Old Persian duvara- "door;" Lithuanian dùrys (plural); Greek thyra "door;" Latin foris "out-of-doors, outside;" Gaulish doro "mouth;" Old Prussian dwaris "gate;" Russian dver' "a door;" Old English dor, German Tür "door," Gothic dauro "gate."

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door (n.)

"movable barrier, commonly on hinges, for closing a passage into a building, room, or other enclosure," c. 1200, a Middle English merger of two Old English words, both with the general sense of "door, gate": dor (neuter; plural doru) "large door, gate," and duru (fem., plural dura) "door, gate, wicket." The difference (no longer felt in Old English) was that the former came from a singular form, the latter from a plural.

Both are from Proto-Germanic *dur-, plural *dures (source also of Old Saxon duru, Old Norse dyrr, Danish dr, Old Frisian dure, dore, dure, Old High German turi, German Tür). This is from PIE root *dhwer- "door, doorway."

Middle English had both dure and dor; the form dore predominated by 16c. but was supplanted later by door. The oldest forms of the word in IE languages frequently are dual or plural, leading to speculation that houses of the original Indo-Europeans had doors with two swinging halves.

Figurative sense of "means of opportunity or facility for" was in Old English. Phrase door to door "house to house" is from c. 1300; as an adjective, in reference to sales, by 1902.

A door is what a dog is perpetually on the wrong side of. [Ogden Nash]
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