“Look, pools are very, very sexy,” continued Mr. Balazs, who said that he plans to spend most of the summer on Shelter Island and in the Hudson Valley. “They’re very sensual—they form, in a weird way, a center. I love water—I’m an Aquarius, but that has nothing to do with it—and I’ve never been away from water in any place.”

Ms. Klein, 50, clad in a simple black dress designed by her ex-husband, Calvin Klein, said that she originally created the book because she was trying to find inspiration for the design of her own pool, and decided to publish it again because “I just thought it wasn’t fair that people couldn’t buy it.” So nice and democratic of her! ((A new first-edition copy fetches about $1,500 on Amazon.)

“I think swimming pools in general are very soothing—the water, the color of the water, the sound of the water, and even just looking at the water,” Ms. Klein continued. “It’s about the architecture: the look of it, the shape of it, the color of it, the reflections of it—that kind of stuff.” She said she no longer has a pool of her own, but does plan to swim in the ocean a lot this summer in East Hampton, where she owns a house.

Mr. Klein, and Vogue editor Anna Wintour, took only brief laps around the room before departing.