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It evokes one of Norway’s icebergs on the outside and the country’s rich tradition of timber buildings on the inside. This is Oslo’s £420m opera house, which was opened by King Harald last Saturday. Its design, which won an international competition, was by local architect Snøhetta, whose £60m Alexandria library in propelled it to international fame in 2002, but whose lighthouse-like Turner museum project for Margate was scrapped after four years and costs that rose from £7m to £50m.

The angular 38,500m2 building appears to float like a stray iceberg in a dock lying just to the west of Oslo’s city centre and opening off a fjord. But rather than ice, its white, shiny surface is travertine marble – a vast 25,000m2 sweep of it – with the crystalline sheer glass walls of the main foyer crashing through it. The roof slopes down along two wide shallow ramps to a wide waterfront plaza, and this is all given over to the public as an architecture-cum-sculpture park.

The view from the waterfront plaza through the window wall reveals a completely different world. Here, beyond the foyer, rises a huge, wave-curled wall of pure natural oak. Not your normal sedate spread of smooth polished oak panels, mind you, but thousands of random vertical oak slats that jostle together in a rich forest of textures and colours.

From the foyer, a pair of oak-lined corridors kink round slatted walls into the main 1,370-seat auditorium. The auditorium adopts a classic horseshoe shape and its decor continues the theme of pure natural oak. But here the vertical slats have been bonded together to produce a smoothly curving balcony front and wall linings. All in the interests of good acoustics, of course.

Oslo’s new venue may have an angular marble roofscape instead of curving precast-concrete sails, but its waterfront site and exhilarating public plaza can’t help but recall a certain other world-famous opera house. And the early indications are that Sydney’s Nordic cousin will be just as widely and enthusiastically received.