1. [v]  fold inwards, of certain organs
2. [v]  sheathe, as in botany; "The chrysalis is invaginated"

INVAGINATE is a 10 letter word that starts with I.

1. \In*vag"i*nate\, v. t.
   To insert as in a sheath; to produce intussusception in.
   
   

2. \In*vag"i*nate\, Invaginated \In*vag"i*na`ted\, a.
   (Biol.)
   (a) Sheathed.
   (b) Having one portion of a hollow organ drawn back within
       another portion.