Some families of semibiplanes (Q1842187)

A semibiplane is a connected finite indicence structure such that every pair of points is incident with 0 or 2 blocks and such that every pair of blocks is incident with 0 or 2 points; the structure is symmetric in that the number \(n\) of blocks equal the number of points and the number \(k\) of blocks through a point equals the number of points in a block. If \(S_1\) and \(S_2\) are semibiplanes with parameters \((v_1, k_1)\) and \((v_2, k_2)\), then there is a general construction of a semibiplane with parameters \((2v_1v_2, k_1 + k_2)\) and particular constructions of semibiplanes with parameters \((v_1v_2, k_1 + k_2 - 1)\), \((v_1v_2, k_1 + k_2)\), \((2v_1, k_1 + k_2)\), \((4^nv_1, k_1 + 3n)\), \((6^n v_1, k_1 + 5n)\), for any positive integer \(n\) depending on the existence of certain polarities in \(S_1\) and \(S_2\).