There's a camphor tree in Eden, with a label reminding visitors of its wonderful scent. They reach out to rub a leaf, but find it shredded; the branches nearest the path are tattered and bare. It's a stark reminder that this Eden is not a paradise for two: 1.7 million people have visited since March, when the complex opened in full, and at times it seems in danger of being a victim of its success.

Tim Smit, Eden's founder and chief executive, says his first love is creating excitement, and this is perhaps the key to Eden's appeal, explaining not only why so many people visit Eden, but also how Smit persuaded an impressive team to work with him and talked funders into parting with £89 million for what may have seemed to be pie in the sky.

Smit originally wanted to showcase Cornwall's tropical plant collections in the Lost Gardens of Heligan, a series of 19th-century gardens that he bought and restored, but he realised he needed more room than Heligan's 80-acre site could offer.

So he turned his local dream into a global project that would represent key climate zones of the world in specially designed modern conservatories. They would be built in a disused clay pit: a dramatic location, giving protection from the weather, but far from ideal. There was no soil, for example - so the team made 50,000 square metres of its own. It flooded, so they devised what Smit calls "the sexiest drains around". And its seriously unstable landscape changed daily as the pit was cleared of clay. This landscape is what inspired the design of the now famous "biomes".

Tim Smit called in Nicholas Grimshaw & Partners, the London architecture practice, for its expertise in working with large glazed structures. It based its first design on perhaps its best-known structure, the wave-shaped steel and glass Eurostar terminal at Waterloo, in London. The design was unable to cope with the shifting shape of the clay pit, however. Back to the drawing board.

The solution Grimshaw and his colleagues came up with was the geodesic dome. Invented in the 1940s by Richard Buckminster Fuller, an American designer and architect, geodesic domes use a spherical lattice - in this case, of hexagons - to support a skin. Simple in form, they maximise internal space and are extremely strong. Most importantly for Eden, the self-supporting nature of a geodesic dome means it can sit on any terrain. Think of soap bubbles settling and adjusting to whatever they land on.

The design of Eden's biomes is led by function. "They're all about minimising the amount of material, minimising the blockage of light, minimising the heat loss," says Jolyon Brewis of Nicholas Grimshaw & Partners.

Glazed traditionally, with glass, a geodesic dome big enough for Eden's collection would be so heavy that it would need a vast steel structure to support it, which would reduce the amount of light reaching the plants. So the architects turned to a modern material: ethylene tetrafluoroethylene, or ETFE, a plastic that lets through much more light than glass and is extremely strong. It is also so light that the tubular steel and ETFE covering of the larger of the two biomes together weigh no more than the air they contain.

Brewis calls the biomes "very modern buildings, unusual in their form, made of steel, quite uncompromising, very functional". He wouldn't call them beautiful; like many architects, he's shy of using a term so hard to define. "The thing that works best," he says, "is the way the biomes lock into the landscape."

Visitors' first view of the biomes is a carefully staged theatrical experience. Invisible at first, they slowly appear over the edge of the clay-pit crater, tantalisingly shielded by the curve of a visitors' centre, which protects the edge of the pit. Walk through the centre's doors and, far below, the biomes gleam white, translucent, seeming to glow from the inside.

They stand out against the scrubby sides of the pit, incredibly clean in this environment. They cling to the pit's sides like fish eggs. They deserve their iconic status. When you stand below, beside them, their size is stunning. They exude mystery: their contents are invisible save for faint outlines and a sense of movement within. There's a hum from heat controllers: something strange is going on.

Inside, the two biomes are quite distinct. The smaller of the two is the temperate zone. Its air is dry and warm, and there's a rocky hillside with sparse Mediterranean plants: rosemary, sage, olive trees. Hillside and plants are a bleached silvery green. Visitors talk in hushed museum voices, looking carefully at the plants, reading the labels.

The excitement comes when you move next door, to the tropical biome, which has generated so much of the fuss about Eden. The dome is huge - at 55 metres, the top seems impossibly far away. It's noisy - a waterfall crashes down from the top, hidden in the vegetation. This time, genteel hush isn't an option. It's also warm and damp, and the plants are immediately impressive: big, lush and densely packed. It's like walking from a two-dimensional film into a three-dimensional one.

"In hindsight," says Brewis, "the humid tropics zone has the effect we wanted it to have. It's big enough to be breathtaking. There's a feeling of space, because the roof's so far above your head. The warm temperate zone, on the other hand, could have been bigger."

He also feels that the interpretation doesn't live up to expectations, but that it's bound to improve as Eden develops. Much of the project was cut, including two additional biomes, when the huge cost of preparing the site became clear.

This is a shame, given the project's mission to promote "the understanding and responsible management of the vital relationship between plants, people and resources, leading towards a sustainable future for all". It is a tall order, and one that smacks of worthiness - although this is something Smit is at pains to avoid. "Eden's not worthy," he says. "People realise we wouldn't have done all this unless we felt really strongly about it. But it's important to wear it lightly on your sleeve. Let people enjoy the sheer joie de vivre."

This exuberance was at the core of Smit's briefs to the design teams. He told the architects he wanted something as recognisable as Sydney Opera House. And he gave a famously succinct brief to Land Use Consultants, the project's landscape architects: "Picasso meets the Aztecs with wow factor 11".

Smit says Eden's power comes from the fact that they were working against the odds. "Everyone on the project will say they've done their best work - they couldn't just busk it; they had to wake up and remember why they became engineers or constructors in the first place."

The determination to create the best is in some ways old-fashioned, Victorian. Eden has such exuberance, confidence, scale and imagination - rare qualities these days - that we don't mind if it fails somewhat to deliver its message, because it makes us grin with pleasure.

Perhaps Eden is even more old-fashioned. Many visitors pass Stonehenge on their way to Cornwall, gazing with awe at the stone circle and marvelling that people put so much planning, effort, time and resources into constructing something so apparently pointless, but also so magnificent. Eden is the same: we don't really know what made Tim Smit build it, but we salute him for it.

The Eden Project is open from 10 a.m. until 4.30 p.m. each day. More details from 01726-811911 or www.edenproject.com. There are connecting buses from St Austell railway station. Further information on accommodation and transport from St Austell Tourist Information Centre (01726-76333). Eden, by Tim Smit, is published by Bantam Press, £25 in UK