As beautiful as the chance meeting between a surfing fish and a horse's head in the atrium of a German bank, Frank Gehry's new conference centre has to be seen to be disbelieved. Stuart Black, thesaurus in hand, was the first reporter to pay a visit.
The receptionist of berlin's DG bank looks absurd. With his desk shunted to one side, he has to scurry to the centre of the anteroom to catch the eyes of the open-mouthed visitors. "Guten Tag! Guten Tag!" he yells. "Kann ich Sie helfen?" But he gets no response – their attention has been captured by the enormous silver biomorph that fills the atrium ahead. One new arrival laughs out loud at what architectural guru Daniel Libeskind has described as "a fish on a wave heading straight for the net".

This is the just-finished DG Bank in Berlin by architect Frank O Gehry & Associates, and its spectacular interior makes no concession to the bureaucracy of signing-in. The central space of the £113m head office is composed of bulging steel and glass, and is at least as good as anything in the Gehry back catalogue.

But what makes this interior doubly stunning is that it arrives so unexpectedly. The bank's new head office is located on Pariser Platz, an area where buildings must defer to the stolid neoclassicism of the Brandenburg Gate. Berlin's planners forced Gehry's exterior to be square and austere. It only dodges being boring because it seems to sulk at the rules that confined it.

To take on the inherent split between his vision and what the twitchy planners will allow, Gehry has had to turn his architecture inside out. Forget the anonymous facade – the visitors do, and quickly – this building is all about innards.

Inside, Gehry picks up the officious formality of the exterior with a rigid frame of offices around an inner courtyard. The five-storey grid, regimented with repeated square windows, suggests an über-bank, a model of efficiency. This provides the context for the three loose and looping central forms. Two of these are huge glass surfaces stretched across the atrium, one at ground level, the other at roof height, one convex, the other concave.

Between the two is the centrepiece: the blobular brushed-steel conference centre, often described, to Gehry's annoyance, as a horse's head. The architect is reluctant to fix a meaning to his creation, but has gone as far as calling it "a prehistoric something".

According to Craig Webb, Gehry's project designer, the idea was "to create an interior landscape, something inspirational and beautiful for the people at work. We realised that the higher execs would have blocks facing onto Pariser Platz, so we wanted something for everyone else."

So, whatever the shapes represent, their reason for being is to make the imagination froth. Two secretaries whose office window stared into the eye of the bulbous beast said it felt "like King Kong was looking in", according to Webb. The poetic structures spoil for a fight with the ordered office grid – the dreamy against the sober, feminine against masculine, fluid against solid.

The construction of the opposing components says it all. Where the office frame was a straightforward concrete structure, the conference centre and glass skirting were massively complex. "When people see it they think it's whimsy," says Webb, "but here we have to be very serious and logical to get it all done."

Using computers to realise the voluptuous forms of his conference centre may be something Gehry has done before, most famously at the Guggenheim in Bilbao, but the process does not seem to have become any easier (see box).

Inside this structure is an unexpectedly intimate space. "The outside is high-tech, the inside low-tech," explains Webb. "We used wood strips that we could bend and overlap. These formed seams on the edges of curves. We created a map for the craftsmen who then fitted everything by hand as if it were a big basket."

The effect is totally different to the molten metal aesthetic on the exterior. It feels organic, albeit an example of nature at its most eccentric. The conference hall set-up within the woven wood strips is a mini-parliament set around a leaf-like oval table. It looks like a war-room for a council of giant ants. "You can't use words to describe the difference between this and a normal hotel hall," explains a DG Bank employee. "It is working within art, another world that you don't want to leave at night."

The swooping glass that floats around the structure posed another set of construction worries. The architect sent a dozen computerised sketches to structural engineer Schlaich Bergermann und Partner to consider. "We developed the clean, continuous shape together," says Dr Jörg Schlaich, senior partner at Schlaich Bergermann. "At first Frank wanted a more extravagant, chaotic roof. But it looked like a crashed Zeppelin – which wouldn't have been good for Germany – so we simplified this into a curve."

Making the structure stand up while keeping the space uncluttered was the stickiest problem. Schlaich's solution involved "spider webs of cables" and four subtle arching ribs. The team opted for a triangular mesh to support the free shape of the glass. This required 1500 panels across the tapered cylinder, each symmetrical pair different to all the others.

The roof is also designed to work as a sculptural element on the exterior. The glass swells up above the rectangular office grid to meet a steel half-moon shaped roof at the back of the building. This is used to divide the bank from the nine-storey apartment block the architect also designed for the site, and marks the schism between the bland facade on Pariser Platz and the more dynamic stonework on the opposite side.

For the apartments, Gehry got away with cutting Italian limestone into a geometric wave that ripples across the building. It is a more dynamic form that tries, along with the two kinetic roof shapes, to rescue DG Bank from its planning straitjacket.

In the interior, the glass and steel sculptures win outright, but outside the dispute is unresolved. From the nearby dome of Foster's rethought Reichstag you can look down and contemplate the conflict – do the roofs represent the arched back of a whale bursting out of its tank, or a sardine forever trapped in its tin?

How did they do it?

Extracting the idea for the conference centre from inside Gehry’s head involved an army of specialists with advanced equipment, but the initial phase was surprisingly low-tech. Before a computer was even plugged in, the architect ordered in a couple of yards of velvet. This was then folded and teased into shape, before melted beeswax was poured over the arrangement and it was transformed into a solid model. Apparently the method was inspired by Italian Baroque artist Gianlorenzo Bernini, who used to coat cloth in plaster for his figure sculptures. After this the machines were brought in – first, a piece of equipment called a faro arm. This has a scanner that digitally records spatial co-ordinates at hundreds of different points on a model. The data was fed into CATIA, a French-designed computer program originally designed to work out the curves for space shuttle hulls. This produced a 3D CAD image. A separate structural engineer, Fischer + Friedrich, was brought in to think about keeping the shape standing up. According to partner Karl Friedrich, the firm had to write a computer program that could translate Gehry’s data for the German system. Apparently this process added nine months to the project – though Friedrich reckons it was still cheaper than buying the requisite software from Nasa. After this, calculations were straightforward and a steel skeleton was designed. The external surface could also be broken up into panels to be manufactured in brushed steel. But since each of these had totally unique double-curving proportions, German firms were reluctant to take on the brief. Eventually Deform, a Swedish firm specialising in industrial fluid tanks, agreed to step in after months of delay. The panels were manufactured through a process called hot-forming. Each panel was shaped separately after being heated to more than 1000 °C and pressed between a pair of cast-iron moulds. The finished panels were fitted by contractor Müller + Altvater. The firm used hydraulic presses to control the material and an infrared device to check the computer-mapped co-ordinates throughout. This was crucial so that when the edges were butt-jointed they matched up with absolute precision.