Résumé : The relations between some quantities related to the Laplace operator are considered. In particular, principal eigenvalue and torsional rigidity are studied in the class of general domains, convex domains, and domains with a small thickness. This allows to obtain a detailed description of the Blasche-Santaló diagram of the two quantities. Several open questions are discussed, in particular when the Laplacian is replaced by the $p$-Laplacian.