ARS COMBINATORIA, cilt.80, ss.205-214, 2006 (SCI-Expanded)
In this paper, we studied that a linear space, which is the complement of a linear space having points are not on a trilateral or a quadrilateral in a projective subplane of order m, is embeddable in a unique way in a projective plane of order n. In addition, we showed that this linear space is the complement of certain regular hyperbolic plane in the sense of Graves [5] with respect to a finite projective plane.