Let \(\pi\) be a finite projective plane of order \(n\). Consider the substructure \(\pi_{n+2}\) obtained from \(\pi\) by removing \(n+2\) lines (including all points on them) no three of which are concurrent. In this paper, firstly, it is shown that \(\pi_{n+2}\) is a B-L plane and it is also homogeneous. Let \(PG(3,2)\) be a finite projective \(3\)-space of order \(n\). The substructure obtained from \(PG(3,2)\) by removing a tetrahedron that is four planes of \(PG(3,n)\) no three of which are collinear is a finite hyperbolic \(3\)-space (Olgun-Ozgir [10]). Finally, we prove that any two hyperbolic planes with the same parameters are isomorphic in this hyperbolic \(3\)-space. These results appeared in the second author’s MSc thesis.
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