  An affine invariant point on the class of convex bodies in R^n, endowed with
the Hausdorff metric, is a continuous map p which is invariant under one-to-one
affine transformations A on R^n, that is, p(A(K))=A(p(K)).
  We define here the new notion of dual affine point q of an affine invariant
point p by the formula q(K^{p(K)})=p(K) for every convex body K, where K^{p(K)}
denotes the polar of K with respect to p(K).
  We investigate which affine invariant points do have a dual point, whether
this dual point is unique and has itself a dual point. We define a product on
the set of affine invariant points, in relation with duality.
  Finally, examples are given which exhibit the rich structure of the set of
affine invariant points.
