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In recent years, the practice has worked its way through various versions of the torus, or elliptical geometry. Now it has come up with something stranger and more complex still for the new £65m Greater London Authority headquarters, which started on site in April across the Thames from the Tower of London.

In shape, Foster's revised design for the GLA building resembles an enormous lop-sided egg. The north side of the egg facing the river sweeps backwards in a bold curve, while the south side tilts outwards in a much steeper curve. It is to be sheathed in a smooth skin of transparent glass, with lesser amounts of anodised aluminium spandrel panels and ceramic-fritted glass near the peak. Carrying out the detailed design for its curtain walling has taxed the minds of Foster's 15-strong design team, with Arup Facades giving technical support, for more than a year. The curtain walling is currently out to tender in two separate packages to Schmidlin of Switzerland and Seele of Germany.

However, it is not component design, manufacture or assembly that is cutting-edge on this project. "The real challenge has been rationalising and simplifying the complicated geometry to the barest minimum of shapes and sizes," says project architect David Kong.

"We found we were being a bit too clever at first," continues Kong. "There was too much information that could have been conflicting. So we have resolved the geometry into a sequence of very simple steps that can be put down on paper and given to the contractor."

The basic aim of the design rationalisation exercise has been to convert the complex spheroidal form into a prismatic form of flat facets in glass and metal supported on straight metal members, all of which can be manufactured relatively simply and therefore cheaply. This involved various intermediate geometrical solutions, all of which had to relate to the building's functional requirements.

As with his design for Berlin's Reichstag, Lord Foster established transparency as the overriding design concept. A skin of clear glass would allow democracy at work in the assembly chamber to be visible to the public.

However, the building's private developer, CIT Group, wanted a green building with low energy consumption. The conventional approach would have been to shade the glass building against excessive solar gain by means of projecting brises-soleil, but this would have undermined the smooth curving form as well as posing maintenance problems.

Instead, solar gain is controlled by manipulating the overall building form into its curious lop-sided shape. The south face of the building, facing away from the river, tilts outwards so that upper storeys project beyond and shade the storeys below. In addition, louvres have been fixed within the outer cavity of a triple-glazed cladding system.

The spheroidal shape has been simplified by slicing it into a series of flat horizontal floor plates. All floor plates are circular in plan, but they diminish in diameter and at the same time offset slightly southwards in alignment as they step up the building.

In addition, to maintain the overall effect of a curvilinear envelope, the facade tilts on each floor. The angle of tilt varies on each floor and on front and rear facades according to two pairs of vertical arcs describing front and back.

Two separate curtain-walling systems have been specified. The bulk of the building, which is devoted to offices, is faced in a conventional stick system of flat glass panels fixed between extruded aluminium mullions. In contrast, the riverfront facade, which encloses the assembly chamber, is enclosed in more transparent frameless glazing.

Predictably, Foster's process of rationalising the geometry has involved complicated CAD modelling, as well as traditional physical modelling in card and perspex. The main problem, however, was to supply a precise set of spatial coordinates for all the curtain wall panels to the contractors for tendering.

"We needed a device that was common to our CAD system and that of the contractor," explains Kong. "So our computer staff worked out a separate mathematical model for calculating the coordinates using simple trigonometry and a spreadsheet. And after that, the contractor went through the whole exercise again using its own CAD system. This exercise flushed out any discrepancies. These amounted to just 0.2 mm over the whole facade, so we were well pleased."