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The symmetry of convex bodies of constant width is discussed in this paper. We proved that for any convex body K⊂ℝ n of constant width, , where as∞(⋅) denotes the Minkowski measure of asymmetry for convex bodies. Moreover, the equality holds on the left-hand side precisely iff K is an Euclidean ball and the upper bounds are attainable, in particular, if n=3, the equality holds on the right-hand side if K is a Meissner body.
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