**Theorem 3.1**: *A cone C(V,S) in PG(3,q) has no flock if and only if S is a blocking set in its carrier plane* .

*Pf*: Since q is at least two, there are at least two planes in any flock of any cone. Suppose that S is a blocking set in , and that and are any two distinct planes of PG(3,q) which do not contain V. If S_{1} is the intersection of with C(V,S), then by lemma 3.1, S_{1} is a blocking set in . The intersection of and is a line *l* in , and so, contains a point of S_{1}. Thus, any two planes not containing V must intersect on the cone C(V,S), and so, C(V,S) admits no flock.

Suppose now that S is not a blocking set. Then there is a line *l* in which contains no point of S. The set of q planes through the line l which do not contain the point V form a flock of C(V,S) (a linear flock ).