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Yet that's exactly what has happened at Kingsdale secondary school in the inner London borough of Southwark. Not that you can see much of that fantasy from its flaking exterior. But step inside and you'll find yourself in a huge, brightly lit arena. Overhead you'll see an extraordinary translucent roof patterned in black, white and silver strips like a 1960s Bridget Riley op art painting writ large. In sunshine, regular geometric shadows are cast by the patterned roof. And at its centre stands a huge timber ball entirely faced in triangular plywood panels. Once inside, this windowless egg-shaped structure reveals itself as an auditorium lined with more triangular plywood panels.

The technological breakthrough, however, is in the translucent roof, said to be the world's largest variable-skin ETFE roof. This means that, quite apart from its mesmerising artistic effect, the membrane responds to changing environmental conditions. The patterns automatically rearrange themselves to vary the amount of daylight entering the atrium, and on hot summer days, this can help keep the temperature in the atrium 9掳C below the temperature outside. As a result, what was an open courtyard is now comfortable enough to serve as a dining hall and teaching space without the expense of heating or cooling it.

Admittedly, the cost of the pioneering roof, the auditorium and the internal refurbishment of nearly half of the existing school amounted to 拢9m, well above the cost guidelines of the Department for Education and Skills. But then the project was set up in 1999 by the Architecture Foundation, a self-styled "architectural catalyst", with DfES backing, as an experimental demonstration project "setting new standards for education architecture". Although the 50-year-old building was crying out for physical improvement, this was not treated as an end in itself but a means to improving and updating the education of the 1100 pupils. Standards had fallen to such a low point that the school had been placed on "special measures" after an Ofsted inspection. The project has since been chosen by the schools building design unit of the DfES as a pilot for the 11 generic "Schools of the Future" designs unveiled earlier this year.

It all began with an architectural competition. "But rather than asking architects to produce design ideas, we asked them to show us how they would engage with the school community," says Sharon Wright of School Works, the foundation's school design group.

The competition was won by fledgling practice de Rijke Marsh Morgan, which entered into the spirit of the competition enthusiastically. "We presented a mock television documentary, with kids queuing up to be interviewed," recalls partner Alex de Rijke. "It was quite a media event."

Having engaged the interest of the whole school community right from the start, the design team spent nine months exploring ideas in a series of workshops with the pupils, teachers and surrounding community, aided by an educational psychologist, educational researcher and performance artist. The pupils came up with significant contributions. "They hated the continuous central corridor round the school," says de Rijke. "So that prompted us to pass the circulation through the central courtyard and open up department hubs in each corner of the building."

After that, dRMM drew up three alternative designs with budgets from 拢5m to 拢11. The intermediate scheme, which proposed roofing-over the courtyard in folded plywood was chosen, with backing by the then schools minister Estelle Morris. The price tag was 拢9m.

But the design process did not end there. "It became apparent that, for that budget, we couldn't radically transform the school and also deal with essential refurbishment to a building that hadn't been touched for 40 years," says de Rijke. "There were the right circumstances to do something extraordinary, but only if we axed certain things like the sports facilities and much of the refurbishment. It was controversial but we managed to carry everyone with us."

Nor did the design for folded plywood roof over the courtyard stand up to scrutiny. Not only would it drastically reduce daylight to the surrounding classrooms, but it would also reflect noise, and require new columns and foundations to support it.

Switching from the folded plywood to pillows of ETFE membrane offered a way out, and as a bonus added a spectacular feature made all the more mesmerising by its rippling geometric patterns (see box story).

The project's other central element is the auditorium, standing near the centre of the atrium. It replaces a single-storey library block that stretched across the courtyard and provided a covered link from one side of the school to another, albeit at the expense of splitting the courtyard into two. Since its conversion to an atrium, the courtyard now serves as a comfortable circulation space, so the auditorium has no need to link both sides of the school. But it still sits on top of an IT study room, a vestige of the former link block which is now half submerged into the floor of the atrium.

The egg-shaped auditorium resembles a giant gourd, windowless and covered internally and externally in birch-faced plywood panels. Not only is this organic form refreshingly non-institutional, but it stands in bold counterpoint both to the transparent, insubstantial atrium roof stretching over it and to the flat panelled walls of the existing school enclosing it.

The auditorium was built and partly engineered by the specialist timber firm Cowley Structural Timberwork, which was responsible for the timber trusses in the assembly hall of the Scottish parliament in Edinburgh. Both in its faceted cladding system of flat polygonal panels and in its underlying structure, it is based on the geodesic domes invented in the 1960s by the visionary American engineer, Richard Buckminster Fuller.

The triangular panals are separated by narrow gaps. Although hidden from sight, the underlying structure combines high-tech engineering with distinctly low-tech carpentry. It consists of short lengths of rough larch logs, joined together at each angle by a round node or knuckle in cast aluminium with projecting steel connectors.

Within the existing school building, the main alteration so far has been to close off part of the central corridor on the top floor and join the classrooms on either side as one large science teaching space. This can be subdivided into smaller spaces by demountable partitions. The enlarged teaching space was only made possible by the conversion of the open courtyard to the covered atrium. The old central corridor has been replaced by walkways that have been erected along the atrium on the first floor, where they are sheltered by the ETFE roof.

The success of the improvements at Kingsdale school has led to the appointment of the same project team to proceed with a second phase. As well as finishing off the refurbishment, it will add two satellite blocks for music and sports. The budget for this is again 拢9m, bringing the total bill to 拢18m. As de Rijke says, "This is comparable with the price for a new school, but it's much bigger, and you get much more for the money."

To head teacher Stephen Morrison, the transformation has had an "extremely positive" effect on education in the school. Replacing long dark corridors with direct walkways through the atrium saves pupils the time that had been wasted traipsing between classrooms, and gone a long way to eradicating antisocial behaviour. Using the atrium as a dining area overlooked by classrooms has reduced the requirement of staff supervisors from 12 to just one. Self-esteem and sense of purpose have also improved.

"Pupils are happier, staff are happier, and we are getting higher quality work," is his contented verdict.