The sleek modern house atop Mt. Rushmore that served as the base of operations for Vandamm (James Mason) is one of the most intriguing houses in cinematic history. Unfortunately, it’s not a real house. No type of structure has ever been (or could ever be) constructed near the top of Mt. Rushmore, as the topography isn’t suitable like the film depicts. It was merely Hitchcock employing his creative license to build a swanky villain base in an exotic and recognizable location - something that generations of action films would mimic in years to come. It also gave the villains a reason to be congregating near Mt. Rushmore, which allowed for the chase scene on the face of the statue. That scene was one of Hitchcock’s primary reasons for making the film.
The exterior of the North by Northwest house is actually a matte painting, which was the standard pre-digital means of combining a shot with artwork to establish a setting. The interiors were constructed and shot on a soundstage. Almost all the interior components are phony; the limestone is largely plaster, the windows didn’t contain glass, and the scenes took place at night to best allow these effects to work.
Wanting the house to be a modernist construction, Hitchcock had it modeled after the architecture of Frank Lloyd Wright, whose homes were the pinnacle of modern design in the 1950s.