“My father hated privet,” said architect Charles Gwathmey in 2002 while making some small tweaks to the 1,200-square-foot house in Amagansett, New York, that he had designed for his parents 37 years earlier. “He thought it was too bourgeois, and not very neighborly.” The house in question, a modernist gem of small-scale living, made Gwathmey famous at the age of 27 and solidified his reputation in a generation of burgeoning architects.

Even after subtle updates—like a new privet hedge—the house maintains the efficient yet spacious feel that helped make it an American icon, especially successful on a regional scale and once described as “more convincing than anything else in the Hamptons.” A separate studio building situated at a 45-degree angle to the house is both satellite and anchor to the residence: Together, they look like a pair of avant-garde but enduring sculptures rising out of Long Island’s flat coastal plains.

Each side of the home is strikingly different, giving the effect of what critic Alastair Gordon called a “Cubist assemblage.”