Etymology
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volute (n.)
1690s, "spiral ornament on an Ionic capital," from French volute (16c.), from Italian voluta, from Latin voluta "a spiral scroll," noun use of fem. past participle of volvere "to turn around, roll," from PIE root *wel- (3) "to turn, revolve." Extended 1756 to any spiral thing or part. As a type of spiral seashell, it is attested from 1753.
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whelk (n.)
marine snail with a spiral shell, Old English weoloc, wioloc, from Proto-Germanic *weluka- (source also of Middle Dutch willoc, Dutch wulk), perhaps from PIE root *wel- (3) "to turn, revolve;" compare volute). The unetymological spelling with wh- dates from 15c.
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*wel- (3)
Proto-Indo-European root meaning "to turn, revolve," with derivatives referring to curved, enclosing objects.

It forms all or part of: archivolt; circumvolve; convoluted; convolution; devolve; elytra; evolution; evolve; Helicon; helicopter; helix; helminth; lorimer; ileus; involve; revolt; revolution; revolve; valve; vault (v.1) "jump or leap over;" vault (n.1) "arched roof or ceiling;" volte-face; voluble; volume; voluminous; volute; volvox; volvulus; vulva; wale; walk; wallet; wallow; waltz; well (v.) "to spring, rise, gush;" welter; whelk; willow.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit valate "turns round," ulvam "womb, vulva;" Lithuanian valtis "twine, net," vilnis "wave," apvalus "round;" Old Church Slavonic valiti "roll, welter," vlŭna "wave;" Greek eluein "to roll round, wind, enwrap," eilein "twist, turn, squeeze; revolve, rotate," helix "spiral object;" Latin volvere "to turn, twist;" Gothic walwjan "to roll;" Old English wealwian "roll," weoloc "whelk, spiral-shelled mollusk;" Old High German walzan "to roll, waltz;" Old Irish fulumain "rolling;" Welsh olwyn "wheel."
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fiddle-head (n.)

also fiddlehead, "one with a head as hollow as a fiddle," 1854 (fiddleheaded), from fiddle (n.) + head (n.). As a name for young fern fronds, from 1877, from resemblance to a violin's scroll. Earliest use is nautical, "carved ornamental work at the bow of a ship in the form of a scroll or volute" (1799).

There are three kinds of heads,—1st The Figure-head is one on which is placed the figure of a man, woman, or the like, &c.; 2d, The Billet-head, or Scroll-head is one finished with two scrolls or volutes ...; and 3d, the Fiddle-head, which is finished with only one scroll or volute, having the spirals turning inwards to the vessel. [Peter Hedderwick, "Treatise on Marine Architecture," Edinburgh, 1830]
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helix (n.)
"a spiral thing," 1560s, originally of the volutes of Corinthian capitals, from Latin helix "spiral, a volute in architecture," from Greek helix (genitive helikos), a word used of anything in a spiral shape (an armlet, a curl of hair, the tendril of a vine, a serpent's coil), which is related to eilein "to turn, twist, roll," from PIE *wel-ik-, from root *wel- (3) "to turn, revolve," from PIE root *wel- (3) "to turn, revolve." The classical plural is helices.
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