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In this talk, we introduce some connections between the Borsuk partition problem and the Vazsonyi problem, two classical and appealing problems in discrete and combinatorial geometry, both related to the Euclidean diameter of bounded sets. The Borsuk partition problem asks whether every set S ⊂ R^d with finite diameter diam(S) is the union of d + 1 sets of diameter less than diam(S). On the other hand, the Vazsonyi problem seeks the maximum number of diameters (pair of points) that a set with n points in R^3 can have. We present an equivalence between the critical sets for the Borsuk problem in R^3 and the critical structures for the V ́azsonyi problem through the use of Reuleaux polyhedra, which are three-dimensional bodies with remarkable combinatorial and geometric properties. This is a joint work with D ́eborah Oliveros and Jorge Ramırez Alfonsın.