On a New Family of Flag-transitive Semibiplanes

Each of the d -dimensional dual hyperovalsSmh discovered by Yoshiara 20 gives rise, via affine expansion, to a flag-transitive semibiplane Af(Smh). We prove that, if m + h = d + 1, thenAf (Smh) is an elation semibiplane. In the other cases, ifd > 2 then Af(Smh) is not isomorphic to any of the examples we are aware of, except possibly for certain semibiplanes obtained fromDn -buildings defined over GF(2). However, many semibiplanes live hidden as quotients inside halved hypercubes. It is thus quite natural to ask whether any of our semibiplanes are like that. We prove thatAf (Smh) is a quotient of a halved hypercube if and only ifh = m.