**Sections**

## Flocks of Arbitrary Cones

Let **S** be an arbitrary set of points in a projective plane embedded in PG(3,q). Let **V** be a point of PG(3,q)\. The *cone* **C = C(V,S)**, with *vertex* V and *carrier* S is the union of the points on the lines joining V to the points of S. is called a *carrier plane* of the cone C.
(Note that we are permitting S to be the empty set which would give rise to the *empty cone*, consisting of just the point V. This is done so that we can develop a consistent terminology at very little cost.)

A *flock* F of cone C is a set of q planes which do not contain V such that no two planes of F meet at a point of C. The intersections of the the planes of the flock with the cone partition the points of the cone except for the vertex V.

**Note** that this definition of flock differs from that found in the majority of the references. The more common definition of a flock refers to the partition of the cone. However, under either definition, the term "*planes of the flock*" refers to the same set of q planes.

Note also that if the cone C is the empty cone, then every set of q planes not containing V is a flock of C.

**Sections**