The Collaborative International Dictionary of English v.0.48:

Exotheca \Ex`o*the"ca\, n. [Nl., fr. Gr. 'e`xw outside + ? a
   case, box.] (Zo["o]l.)
   The tissue which fills the interspaces between the cost[ae]
   of many madreporarian corals, usually consisting of small
   transverse or oblique septa.
   [1913 Webster]