**Theorem 11.2.4**: *Let F = F(t ^{a}, t, t^{b}) be a monomial semi-field type flock in PG(3,q) with q = p^{n} for some prime p, a = p^{i}, b = p^{j} with 0 < i < j < n. Let d = gcd(i,j,n). Then the critical cone of F is thick.*

*Pf*: In the dual setting, the critical cone of a Flock is represented by the largest set of lines of W' = 0 which do not pass through any of the points where lines joining two points of D_{F} meet W' = 0. In order for the cone to be thick, there should be no set of less than [q+2/2] collinear points in W'=0 through which all the lines of D_{G} must pass. Alternatively, no set of at least q+1 - [q+2/2] = [q+1/2] collinear points of W'=0, through which no D_{G} line can pass. Let **S** be the set of points of W'=0 where lines joining two points of D_{F} meet W'=0. By Proposition 11.2.5 , there are (q-1)/(p^{d} -1) < q + 1 points in S, and so, through each point of W'=0 not in **S** there must pass lines which do not intersect **S**. A line which intersects **S** in at least two points must intersect it in p^{d} + 1 points. Notice that we must have d < n/2, otherwise F is a star flock. It now follows that since p^{d} + 1 < [p^{n} + 1/2], any set of collinear points of **S** has fewer than [q+1/2] points and so the critical cone of F must be thick.