She sits puffing Marlboro Lights, from a leather cigarette case, lit by a chunky green cast-glass lighter, in her Clerkenwell studio. She is swathed in black Issey Miyake, as ever. She's fighting a cold, but she's on top form, enthusing about the new-found liveliness of London. She chats about the zone - how the flicked-up, mirrored entrance canopy has turned out even better than she'd hoped, how it sets off the wiggly, brain-related Richard Deacon sculpture that hovers overhead as you go in. "It multiplies - you can't tell where one thing ends and another begins." She's also keen on the other commissioned artworks there, such as Ron Mueck's Giant Boy, a typically hyper-realistic, superscaled crouching figure that gazes at you intently on one of the upper levels. "From the start of this project, we thought we should involve artists in the installation - because there are some great British artists, especially dealing with ideas of the mind. Thinking not just about scientific exploration, but also spatially; triggering thoughts about how you perceive things. That's very important."

For Hadid, the Mind Zone, with its glass-floored ramps and interconnecting spaces and levels, is a continuation of her perpetual refinement of what she calls "interior urban spaces". The aim, she says, is to achieve a seamlessness: seamlessness of walls, floor and ceiling, but also integration of display space with circulation space and integration of architecture with exhibition displays and artworks so that the whole thing reads as one design.

As part of the process, she has worked with others - Doris Saatchi on the selection of artists, Neville Brody on the graphics, Mark Cousins on the exhibition content (there's a "robot zoo", for instance, to be seen in there, along with "morphing machines" that can show you as a different race or sex). This collaboration was, she admits, a learning curve, but they achieved the necessary seamlessness.

But nobody involved in the Dome - with the possible exception of the freebooting caricaturist Gerald Scarfe (see opposite) - has enjoyed a bed of roses. "I must say, it's not been an easy ride," Hadid concludes. "The time limits put us under tremendous pressure, but that created its own dynamic. I think the building got better, actually. They understood what we were trying to do. We have nothing to complain about."

Hadid, after all, is a notorious perfectionist. Nothing to complain about? One senses pigs flying down in Greenwich. This, if anything, is a good augury for the Dome.