Generalized Quadrangles of Order 4. II

Recall that if Y is a GQ of order 4 not isomorphic to W(4), then each pair of nonconcurrent lines (or noncollinear points) belongs to a triad with three centers, and each with three centers has exactly three centers. Moreover, if 9 = (L, , L, , &) and AZ = (1M, , M, , MJ are orthogonal triads of lines, the pair (9, A) must be of type a, i.e., no secant passes through two special points. Moreover, each secant must pass through a unique special point. Throughout the remainder of this note we let Y denote a GQ of order 4 that is not isomorphic to W(4), and 9 = (L, , L2, LJ and A? = (MI , Mz, Ma denote an orthogonal pair of triads of lnies. The notation and terminology of [l, Sect. 21 will be used in so far as it is appropriate: xij = Li n iWj ; R = {xij 1 1 < i, j < 3}. Other notation will be recalled as needed.