The School of American Ballet yesterday unveiled its newly christened Lincoln Kirstein Wing, designed by Elizabeth Diller of Diller Scofidio + Renfro, the firm that is in charge of the larger redevelopment project at Lincoln Center. The $7.2 million expansion turned two studios into four by raising the ceilings and adding two new studios that “float” (i.e., are supported by massive steel beams) over the original ones. Double panes of glass keep out sound from the neighboring studio, and liquid crystal glass on the walls of the floating studios allow for observation, or privacy, as teachers wish.

The project is the first element of Lincoln Center’s massive redevelopment to be completed. The two major phases — the West 65th Street Project, with a budget of $650 million, and the Promenade Project, with a preliminary budget of $160 million, are scheduled to be completed for Lincoln Center’s 50th anniversary in 2009-2010. Lincoln Center is also renovating the privately owned public space across Columbus Avenue known as the Harmony Atrium, with a design by Tod Williams Billie Tsien Architects.

Ms. Diller said that she and SAB artistic director Peter Martins easily understood each other in talking about the project. “We kind of do the same thing: We’re interested in bodies in space and trying to defy the laws of gravity,” she said.