The Collaborative International Dictionary of English v.0.48:

Theca \The"ca\, n.; pl. Thecae. [L., fr. Gr. ? a case to put
   anything in. See Tick a cover.]
   1. A sheath; a case; as, the theca, or cell, of an anther;
      the theca, or spore case, of a fungus; the theca of the
      spinal cord.
      [1913 Webster]

   2. (Zool.)
      (a) The chitinous cup which protects the hydranths of
          certain hydroids.
      (b) The more or less cuplike calicle of a coral.
      (c) The wall forming a calicle of a coral.
          [1913 Webster]