Divisible points of compact convex sets

By associating with an affine dependence the resultant of a related probability measure, we are able to define the set of divisible points, D(K), of a compact convex set K. Some general properties of D(K) are discussed, and its equivalence with a set recently introduced by Reay for convex polytopes demonstrated. For polytopes, D(K) is a continuous image of a projective space. A conjecture concerning D(K) is settled affirmatively for cubes.