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We consider a typical (in the sense of Baire categories) convex body K in R d + 1 . The set of feet of its double normals is a Cantor set, having lower box-counting dimension 0 and packing dimension d. The set of lengths of those double normals is also a Cantor set of lower box-counting dimension 0. Its packing dimension is equal to 1 2 if d = 1 , is at least 3 4 if d = 2 , and equals 1 if d ≥ 3 . We also consider the lower and upper curvatures at feet of double normals of K, with a special interest for local maxima of the length function (they are countable and dense in the set of double normals). In particular, we improve a previous result about the metric diameter. |
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