1-convex games have been introduced by Theo Driessen in his 1985 PhD dissertation. They form an interesting class of games for at least one reason: the core of a 1-convex n-player game is a regular simplex of dimension n – 1 or a single point. As a consequence, its nucleolus is the center of gravity of the core. We recall and extend the results obtained by Driessen and provide examples and applications.