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I stand at the foot of the erotic gherkin, now under construction a stone's throw from the Lloyd's building in the City of London.

It looks neither organic nor particularly sexy.

But it certainly is big, bulging slightly outwards at the waist as it bursts through the lower ranks of boxy City office blocks. When completed early in 2004, it will taper to a cone-shaped pinnacle containing a restaurant 180 m above the pavement.

This is Foster and Partners' Swiss Re headquarters, which does for the City what Foster's Greater London Authority headquarters does for the South Bank – combining 21st-century curvilinear geometry with energy-efficient office space.

At 41 storeys, the Swiss Re tower is just one short of the City's tallest building, Tower 42. It is also much wider, with a maximum diameter of 57 m, packing in 76,400 m2 of gross floor area. The building's curves, however, disguise its bulkiness. A spokesperson at Foster and Partners explains: "The tower appears more slender than a rectangular block of equivalent size. Reflections are reduced and transparency improved, and the slimming of its profile towards the base maximises the public realm at ground level."

The spiral geometry also has structural and environmental benefits. A diagonal grid of tubular steel members at the perimeter provides support and bracing, creating a column-free floorplate between the external wall and central core.

Six atriums spaced around the perimeter of each floor will spiral diagonally up the height of the tower – the beginnings of which are visible in the photograph, left. When the atriums are filled with plants they will coalesce to form a helter-skelter effect of "gardens in the sky".

As they are naturally ventilated, the atriums will also act as large flues, bringing fresh air into the office space and reducing air-conditioning by up to 40%.

These spiralling gardens will be enclosed behind the tower's flush glass skin and will only be visible from the outside when lit up at night. Perhaps then the building will actually live up to its organic nickname.