Volume approximation of smooth convex bodies by three-polytopes of restricted number of edges - Böröczky, Károly J.; Gomis, Salvador S.; Tick, Péter (Monatshefte für Mathematik, 2008)
. For a given convex body K in 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.