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math.MG2013★ 6 cited
A point in a -Polytope is the barycenter of points in its -faces
Michael Gene Dobbins
Using equivariant topology, we prove that it is always possible to find points in the -dimensional faces of a -dimensional convex polytope so that their center of ma…
math.MG2013
Regular systems of paths and families of convex sets in convex position
Michael G. Dobbins, Andreas F. Holmsen, Alfredo Hubard
In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of eac…