The two stayed close, swapping inspirations and visiting when they could. At 25, she married a fellow Monegasque she’d known since childhood, someone as eccentric as she, and moved to a grand apartment in a high-rise overlooking Monte Carlo’s harbor. They spent their time traveling the world, befriending artists such as the surrealist American photographer Joel-Peter Witkin and the Italian post-Memphis sculptor Andrea Branzi. Along with Dixon’s work, they amassed pieces by other emerging radical designers of the late 20th century, including the London-based sculptor Ron Arad and the Dordogne, France-based furniture maker André Dubreuil, who fashioned giant clocks and imposing Asian lanterns that appeared both gothic and futuristic. “She was really one of the first adopters of post-postmodern punky stuff,” Dixon says.

Meanwhile, the designer had made a name for himself. After creating the sinuous S chair and licensing it to Cappellini in 1990, his subsequent pieces, including the 1996 polyethylene Jack, a stackable lamp that resembles a cartoon version of the classic metal toy, established Dixon as a juggernaut of industrial design. In 1998, he was named the creative director of Habitat, the then foundering British furniture conglomerate begun in the 1960s by Sir Terence Conran. Dixon ran it until 2008, when he left to launch his eponymous brand of mostly metal (often copper) lighting, chairs and other furnishings.

ONE NIGHT IN 2010, while he and the woman from Monte Carlo were having dinner in London, she offered Dixon a commission that would test even his robust enthusiasm for learning on the job. She and her husband wanted him to design a villa for them on a spectacular cliff-side site just yards beyond the principality’s border in Cap d’Ail, France. At the time, the spot was occupied by a sort of shepherd’s hut surrounded by lemon trees, built in the late 19th century by her great-grandfather. Her family used it as a getaway from the city; she had spent summers there as a teenager, picking tomatoes and looking after an aging tortoise.

Dixon had visited the property in the 1980s, after the woman had taken it over from her father; he had even made some custom furniture for it. But that was far different than designing a residence from the ground up for a client with notoriously outré tastes. Though he had developed an interior design practice alongside his product empire, he had no architectural training. But such concerns didn’t faze the woman. She didn’t even feel the need to give him much direction. “Tom knew me,” she says. “He knew what I liked. I knew he was the person to make it.”