Approximation of General Smooth Convex Bodies

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The Spherical Convex Floating Body (2014, unknown): “For instance, affine surface area appears in best and random approximation of convex bodies by polytopes, see K. Böröczky Jr. [11] [12], P. M. Gruber [26] [27] [28], M. Ludwig [38], M. Reitzner [59] and C. Schütt [68] [70].”
Thrifty approximations of convex bodies by polytopes (2012, background): “…for all suﬃciently small 0 ǫ ǫ 0 ( C ) one can obtain an approximating symmetric polytope with at most ( γ/ǫ ) ( d − 1) / 2 vertices for some absolute constant γ > 0, and the dependence on ǫ cannot be made better [G93b], [B¨o00] (note that the upper bound for ǫ depends on the convex body C ).”