One of New York’s most synergistic and urbanistically conversant buildings is going up on Cooper Square. Though the new structure contains laboratories, studios, and classrooms to accommodate the art, architecture, and engineering programs at Cooper Union, it’s hardly academic. It also represents the stunning New York debut of its architect, Thom Mayne, a 64-year-old Pritzker Prize laureate who is the principal of the Los Angeles firm Morphosis.

“It’s not a one-idea building,” Mr. Mayne said during a recent interview at his New York office. “The easy ones are just one big idea — you look at it and get it. This building is much more complicated.”

With ground broken and construction underway, the $130 million building’s opening will coincide with the 150th anniversary of the Cooper Union for the Advancement of Science and Art in February 2009. With a scale similar to the nearby 1859 Foundation Building, it faces Third Avenue between 6th and 7th streets, its glassy back facing the St. George Ukrainian Catholic Church on Taras Shevchenko Place. Many in the Ukrainian community were initially opposed to nine floors replacing the drab, two-story 1912 Hewitt Building, but the renderings showed the structure to have such lightness, permeability, and transparency that the community eventually surrendered to it, amicably.

A sneak peak of what’s to come from renderings expose a playful, quirky façade of glass and perforated metal skin that changes throughout the day. The building senses sunlight and adjusts the interior climate. The porous panels, which can also be controlled by students and teachers in classrooms, were modeled after the mechanical screens that have worked so well at Morphosis’s previous project, a California Department of Transportation district headquarters in Los Angeles. The lovely luster of the Cooper Union building offers a contrast to the dull bricks of the surrounding 19th-century buildings (although there are soaring glass neighbors — Charles Gwathmey’s condominium tower on Astor Place and the upcoming Cooper Square Hotel one block south).

The ground floor of the soon-to-rise university building, dedicated to community retail space, is set back from the street; the rest of the building is hoisted atop V-shaped pillars and appears to float. The dynamic façade caves in and features a glorious gash revealing the building’s most arresting feature: a curvaceous atrium. The architect refers to it as a “stacked vertical piazza,” and the atrium swirls all the way up to the skylit ceiling.

There’s a sinuous grand staircase, but sky bridges crisscross above. Sure, there are elevators, but they only stop on the 4th and 7th floors, where there are lounges and meeting areas. “It produces interactions so that three departments are all mingling together,” the architect said. “It’s going to promote lots of activity.”

Mr. Mayne, who teaches architecture at the University of California, Los Angeles, has already designed other academic buildings — his most famous being the breakthrough Diamond Ranch High School in Pomona, Calif. A fragmented building that feels like a futuristic playground, it’s quite simply the coolest place to be for acne-ridden adolescents. The building was used in several big-screen films, including “The Cell.”

For the high school, and as a starting point for all of his projects, Mr. Mayne said he asks himself the question: “How does our work challenge existing paradigms and expand ideas of what architecture is and isn’t?”

His process thrives on context — he is always thinking in terms of connective tissue, so that his buildings’ boundaries reach well beyond their physical sites and allow the cityscape to seep in.

“I’m not a tabula rasa type,” Mr. Mayne said. “In some ways, the more constraints I have, the work is more interesting to me. I think some of our best work has been with projects that come with complicated conditions.”

Mr. Mayne, who spent most of his career in Los Angeles, said he identifies strongly with New York, where he now resides. “New York is this cacophony — a collection of radical differences, an agreement of non sequiturs.” Mr. Mayne, who’s as good with words as he is with buildings, said. “The diversity and intensity are startling.”

The energy of the Cooper Union structure, he said, should spill out into the streets. “One of the things about working here in New York is that you want to be one of the people that mixes up the status quo, and it’s an incredible challenge,” he said. “We want to hit all the right notes precisely because it’s our first building here.”