The Aquatics Centre's beauty will only be revealed once its Olympic add-ons are gone

Zaha Hadid's architecture has always been grandly expressive. It doesn't do modest, or subtle. But her Aquatics Centre, long heralded as the brand-mark building for the 2012 London Olympics, turns out to be something else entirely: stealth architecture, a dull shell concealing something dazzling.

The sensational wave-form of the £268m building has been traduced by vastly lumpen side-saddles, whose grandstands will more than quadruple audience numbers during the Games. It's like forcing the lithe Olympian swimmer Fran Halsall to attempt a world freestyle record with two bargain-basement rucksacks strapped to her hips.

The Olympic Delivery Authority can hardly be blamed for wanting to pack 17,500 spectators into the building, even if it was designed for 3,000. But the result, as seen from the outside, is bemusing: you might not think the Aquatics Centre was architecture at all, let alone anything to do with sport. The blunt fact is that the Centre's true architectural dynamics won't be seen until this gubbins is stripped away, to put the building in post-Olympic "legacy" mode.

The external appearance of the building makes a mockery of the practice's official description of the design being inspired by the fluid geometries of water in motion, creating spaces and a surrounding environment that reflect the riverside landscapes of the Olympic Park. The key design move is an undulating roof that sweeps up from the ground in a vast ripple, enclosing the pools of the Centre with what is described as "a unifying gesture of fluidity". Not from the outside, it doesn't.

Inside, though, the Aquatics Centre is pure, awesome theatre. As the British diver Tom Daley held court in the stands yesterday, Hadid revealed the simplicity of her design vision: "The intention was always to make a stunning roof – a wave, water, some kind of sea-life creature."

The creature is 160 metres long, with a maximum width of 90m. There are no visible columns holding up the 3,200 tonnes of steel and 70,000 bolts, and the manta ray swoop of the roof is supported on only three points: two relatively slim concrete cores near the northern end of the building and a concrete wall at its southern end. These structural anchors are concealed in the flow of the structure and are barely noticeable to spectators, which means that the drama of the roof form is utterly dominant.

The drama has a functional purpose: the roof undulates to define the spaces around the 10-lane competition pool and the diving pool. The roof projects beyond the arena, giving the structure quirky brims at its end.

The geometry of the roof and the concrete waists of the arena are complex, and finished to absolute perfection – a tribute to the contractor, Balfour Beatty, and to Finnforest, which supplied the 35,000 lengths of timber that line the underside of the roof with not so much as a waver in their lines of trajectory. The concrete is silky to touch and would satisfy even the great master of swerving cement, Oscar Niemeyer. No doubt about it, this is Rolls-Royce construction, even if the huge amount of steel in the roof happens to weigh as much as 2,800 Ford Fiestas.

As always with Hadid's buildings, the structural gymnastics are at least as interesting as the architecture. When large buildings have shapes as challenging as this, the big question is quite simple: how did they do it? If you look at cross-section drawings of the Aquatics Centre, it is the amount of steel in the double curve of the parabolic roof that hits you in the eye. Everything else about the structure looks skimpy in comparison.

It wasn't just the 3,200 tonnes of steel in the roof that was challenging, but the forces of structural tension and compression generated by its geometry. This was meat and drink, however, to Hadid's engineers, Arup.

The roof's steel trusses, some of them 40m long and weighing 70 tonnes, were erected on giant temporary trestles. When half the roof structure had been completed, one section of the trestles was removed, to allow the pit of the diving pool to be dug. This meant that the roof had to be jacked up above the trestles and held until the pool excavations were complete. And then it was jacked up a second time before being lowered into its final position. At this rather critical point, one assumes even Arup's gaffers held their breath.

The Aquatics Centre is undoubtedly a structural marvel. But because it is a building designed for two purposes – Olympic and post-Olympic – it does not yet have the sheer mojo of, say, Pier Luigi Nervi's exquisite roof structure at Rome's Palazzetto dello Sport. That building looks absolutely riveting, outside and in. It is simply too soon to make any sensible judgement of the architectural quality of Hadid's core building, because we can only fully experience its interior. She, and her project architect, Jim Severin, have given considerable attention to the landscaping immediately around the arena, but this too is not yet evident.

Nevertheless, the Aquatics Centre joins Hopkins Architects' sleek Velodrome as one of the two architecturally ambitious landmark buildings on the Olympic site. They deliver world-class sporting facilities to east London and they will undoubtedly inspire tens of thousands of people to take swimming and cycling more seriously in the next decade or two.

The great Japanese architect (and stadium designer) Kenzo Tange said: "Architecture must have something that appeals to the human heart." It is that direct appeal to the heart that is temporarily crushed by the Aquatics Centre's bloated seating pods. Until after the Olympics, it must remain Jekyll and Hyde architecture, puzzling and mall-like on the outside, yet thrilling enough inside to make Fran Halsall's heart beat a little quicker when she tenses on her starting block, seconds before the start of the 100m freestyle final next summer.

Going for gold: Great Olympic structures

Berlin Olympic Stadium (1936)

Designed by Werner and Walter March, the stadium glorified Nazism. However, its architecture was an innovative mixture of order and surprise. The facade, barely three storeys high, concealed the fact that the seating descended into a deeply dug bowl.

Palazzetto dello Sport, Rome (1960)

Sheer design genius, by the engineer Pier Luigi Nervi, and decisive proof that ferroconcrete can be beautiful. The ribbed concrete dome is 61 metres wide, braced by flying buttresses. It was built in only 40 days.

Tokyo Olympic Stadium (1964)

Who said Brutalist architecture was ugly? Kenzo Tange's stadium was built in the form of two semi-circles, slightly displaced, with a roof composed of steel cables carrying enameled steel plates.

Munich Olympic Stadium (1972)

The stadium's sweeping acrylic and steel cable canopies, designed by the ex-fighter pilot Frei Otto and Gunter Behnisch, were architecturally revolutionary and came to symbolise Germany's democratic transparency and optimism.