Let K be a convex body in \({\mathbb {R}}^{n}\) . The Santaló point of K is the unique minimizer on \({\textrm{int}}(K)\) of the function \(u\mapsto {\textrm{vol}}_{\textrm{n}} ((K-u)^{\circ })\) , where \(Q^{\circ }\) denotes the polar convex body of Q and “ \({\textrm{vol}}_n\) ” is the n-dimensional volume. In a sense, the Santaló point plays the role of a central point of K. This work studies a variant of such a concept of centrality: we change volume by diameter. The theory of “diametral” Santaló points diverges from the classical theory in a number of ways.
