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Werner, Mathieu Meyer","submitted_at":"2013-10-01T02:56:06Z","abstract_excerpt":"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)).\n  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).\n  We investigate which affine invariant points do have a dual point, whether this dual point is unique and has itself a dual point. 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