Some Properties of the Yoshiara Family of Planes

In [4], Yoshiara constructed a family of q + 3 planes inPG (5, q), q even, satisfying certain intersection properties. This is then used to construct extended generalized quadrangles of order (q + 1, q − 1). In this note we examine the properties of these planes and show that the existence of a set of q + 2 planes satisfying the intersection properties necessarily implies the existence of the (q + 3)th plane, and that two such families meet in at most (2 q + 6) / 3 planes. We also pose some open completeness problems.