The Collaborative International Dictionary of English v.0.48:

Triplicity \Tri*plic"i*ty\, n. [Cf. F. triplicit['e], fr. L.
   triplex, triplicis, threefold. See Triplicate, a.]
   The quality or state of being triple, or threefold;
   trebleness.
   [1913 Webster]

         In their trinal triplicities on high.    --Spenser.
   [1913 Webster]

WordNet (r) 3.0 (2006):

triplicity
    n 1: (astrology) one of four groups of the zodiac where each
         group consists of three signs separated from each other by
         120 degrees [syn: triplicity, trigon]
    2: the property of being triple