Getting to the groundbreaking for the Montauk Playhouse Community Center’s new aquatic center was reminiscent of the concept of “third places,” said Sarah Iudicone, the Playhouse Foundation’s president. After home and work, “third places play an important part in our identity. They allow us to open ourselves up, learn more about the people around us, and deepen our civic engagement. And because of all of your support, Montauk is going to have a new third place.”