The Collaborative International Dictionary of English v.0.48:

Verticality \Ver`ti*cal"i*ty\, n.
   The quality or state of being vertical; verticalness. [R.]
   [1913 Webster]

         The different points of the verticality. --Sir T.
                                                  Browne.
   [1913 Webster]

WordNet (r) 3.0 (2006):

verticality
    n 1: position at right angles to the horizon [syn:
         verticality, verticalness, erectness, uprightness]