1857, "full of windings," from twist (n.) + -y (2). Meaning "attractively feminine," 1970s slang, is from twist "girl" (1928), apparently from rhyming slang twist and twirl (1924).
had to steer the car down a twisty track
twirler
twist
twisted
twister
twist-off
twisty
twit
twitch
twitter
twitterpated
twizzle
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