Maybe it’s the hexagonal geometry, maybe the stepped levels, maybe the way it rises out of a hillside that – before the pine trees grew too tall – looked over the Durham Freeway. Whatever it is, from the outside it’s an icon of Research Triangle Park and, on Saturday, you can see how it looks inside.

Triangle Modernist Houses, the society that Smart formed for fans of Modernist architecture, has arranged for building tours between 9 a.m. and 1 p.m., the first time the building has been open to the public in more than 30 years.

GlaxoSmithKline, which got the building through a 1995 merger, sold it in June to its RTP neighbor United Therapeutics. The new owner plans a major renovation, the interval until then allowing a “tiny window” for touring, Smart said.

Burroughs Wellcome, a British pharmaceutical company, commissioned architect Paul Rudolph to design its U.S. headquarters at RTP in 1969. One of the most renowned American architects of the 1950s and 1960s, Rudolph developed his design from a basic A frame, with terraced floors to suggest an extension of the hill it would be built on.

In 1981, Hollywood producers used the building for a set in the science-fiction movie “Brainstorm,” actress Natalie Wood’s last movie.

Formally, its name is the “Elion-Hitchings Building,” to honor two Burroughs scientists who won a Nobel Prize in 1988. Over the years, though, it’s been called a “beehive,” “honeycomb,” “ziggurat” and “spaceship.”

In 1989, a New York Times writer described it as “reminiscent of a medicinal tablet.”

Smart said Burroughs Wellcome wanted its headquarters to be “the most avant-garde building in the Triangle, which it really was for the time.” Its flying terraces “were all very forward-looking ... to embody the future of medicine.”

Rudolph carried the angular theme inside, even to specifications for carpet. Tourgoers will start in the lobby, which Rudolph biographer Roberto De Alba ( bit.ly/THV55r) described as “a thing of the future.

“The space soars, exposing three levels of balconies, which maintain the diagonal lines of the A-frame,” De Alba wrote, and summed up the interiors as “simply stunning.”

From the lobby, the tour goes through the auditorium – “kind of normal now, but it was advanced for the time,” Smart said. Then the “gorgeous, absolutely gorgeous” company cafeteria, then up to the fifth-floor executive suites with their terraces and back down past a few offices.

Remarkable as the interior’s aesthetics may be, its utility as office space was “not always the most practical,” said Smart, and tourgoers will see some attempts, “usually unsuccessful,” to improve things.

And, like a lot of buildings of the time, the HVAC systems never worked very well, either.

The new owner, United Therapeutics, paid $17.5 million for the building and surrounding land, though Durham County’s tax office values them at only $11.4 million. UT plans to demolish most of the expansion structures added after the building opened in 1972, but, Smart said, “has made a commitment to preserve the original structure.

“Which is great.”