Some families of semibiplanes Original Research Article

A semibiplane is a connected finite incidence structure satisfying (i) every pair of points are incident with 0 or 2 blocks (ii) every pair of blocks are incident with 0 or 2 points. We give several constructions for combining semibiplanes to produce new ones. Some of these constructions are iterative and some require the input semibiplanes to have special properties (such as divisibility, regular automorphism groups, polarities). There are two well-known constructions which supply infinite families of semibiplanes with the properties we require: one based on involutions in projective planes, the other having point set and block set being the vectors of Vn(2). We review these constructions and show how our methods may be used to construct several more infinite families of semibiplanes.