The Collaborative International Dictionary of English v.0.48:

Perpendicularity \Per`pen*dic`u*lar"i*ty\, n. [Cf. F.
   perpendicularit['e].]
   The quality or state of being perpendicular.
   [1913 Webster]

WordNet (r) 3.0 (2006):

perpendicularity
    n 1: the relation of opposition between things at right angles
         [syn: orthogonality, perpendicularity, orthogonal
         opposition]
    2: the quality of being at right angles to a given line or plane
       (especially the plane of the horizon)