The Collaborative International Dictionary of English v.0.48:

Quaternity \Qua*ter"ni*ty\, n. [LL. quaternitas, fr. L. quaterni
   four each: cf. F. quaternit['e].]
   1. The number four. [Obs.] --Sir T. Browne.
      [1913 Webster]

   2. The union of four in one, as of four persons; -- analogous
      to the theological term trinity.
      [1913 Webster]

WordNet (r) 3.0 (2006):

quaternity
    n 1: the cardinal number that is the sum of three and one [syn:
         four, 4, IV, tetrad, quatern, quaternion,
         quaternary, quaternity, quartet, quadruplet,
         foursome, Little Joe]