Floating and Illumination Bodies for Polytopes: Duality Results
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🧮 math.MG
math.FA
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bodyfloatingilluminationpolarpolytopesresultsaffineapproximated
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We consider the question how well a floating body can be approximated by the polar of the illumination body of the polar. We establish precise convergence results in the case of centrally symmetric polytopes. This leads to a new affine invariant which is related to the cone measure of the polytope.
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