The Collaborative International Dictionary of English v.0.48:

Cock \Cock\ (k[o^]k), v. t. [imp. & p. p. Cocked (k[o^]kt); p.
   pr. & vb. n. Cocking.] [Cf. Gael. coc to cock.]
   1. To set erect; to turn up.
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            Our Lightfoot barks, and cocks his ears. --Gay.
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            Dick would cock his nose in scorn.    --Swift.
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   2. To shape, as a hat, by turning up the brim.
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   3. To set on one side in a pert or jaunty manner.
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            They cocked their hats in each other's faces.
                                                  --Macaulay.
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   4. To turn (the eye) obliquely and partially close its lid,
      as an expression of derision or insinuation.
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   Cocked hat.
      (a) A hat with large, stiff flaps turned up to a peaked
          crown, thus making its form triangular; -- called also
          three-cornered hat.
      (b) A game similar to ninepins, except that only three
          pins are used, which are set up at the angles of a
          triangle.
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WordNet (r) 3.0 (2006):

cocked hat
    n 1: hat with opposing brims turned up and caught together to
         form points