Characterising elliptic solids of Q(4,q), q even

Let E be a set of solids (hyperplanes) in PG ( 4 , q ) , q even, q > 2 , such that every point of PG ( 4 , q ) lies in either 0, 1 2 ( q 3 − q 2 ) or 1 2 q 3 solids of E , and every plane of PG ( 4 , q ) lies in either 0, 1 2 q or q solids of E . This article shows that E is either the set of solids that are disjoint from a hyperoval, or the set of solids that meet a non-singular quadric Q ( 4 , q ) in an elliptic quadric.