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]

Moby Thesaurus II by Grady Ward, 1.0:

39 Moby Thesaurus words for "intricacy":
   abstruseness, arduousness, bothersomeness, burdensomeness,
   complexity, complexness, complication, convolution, crabbedness,
   crampedness, deepness, difficultness, difficulty, entanglement,
   esoterica, hairiness, hardness, intricateness, involution,
   involvement, knottiness, laboriousness, onerousness,
   oppressiveness, perplexity, profoundness, profundity, ramification,
   reconditeness, rigor, rigorousness, ruggedness, strenuousness,
   subtlety, tanglement, technicality, toilsomeness, toughness,
   troublesomeness