The Collaborative International Dictionary of English v.0.48:

Intricacy \In"tri*ca*cy\, n.; pl. Intricacies. [From
   Intricate.]
   The state or quality of being intricate or entangled;
   perplexity; involution; complication; complexity; that which
   is intricate or involved; as, the intricacy of a knot; the
   intricacy of accounts; the intricacy of a cause in
   controversy; the intricacy of a plot.
   [1913 Webster]

         Freed from intricacies, taught to live
         The easiest way.                         --Milton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

intricacy
    n 1: marked by elaborately complex detail [syn: elaborateness,
         elaboration, intricacy, involution]