Volume approximation of smooth convex bodies by three-polytopes of restricted number of edges. (English summary) Monatsh. Math. 153 (2008), no. 1, 25–48. Summary: “For a given convex body K in R 3 with C 2 boundary, let P c n be the circumscribed polytope of minimal volume with at most n edges, and let P i n be the inscribed polytope of maximal volume with at most n edges. Besides presenting an asymptotic formula for the volume difference as n tends to infinity in both cases, we prove that the typical faces of P c n and P i n are asymptotically regular triangles and squares, respectively, in a suitable sense.
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