The Saudi billionaire Alwaleed bin Talal announced this week that he wants to build a skyscraper a kilometre high. It would have a Four Seasons hotel and a 157th-floor terrace. High-speed, double-decker elevators would rush visitors to the top levels in barely a minute and a half. The projected “Kingdom Tower” in Jeddah would rise higher than Burj al-Khalifa, the 828-metre colossus that has been, since it opened in Dubai in January, the world’s tallest building.

Ambitious plans for big skyscrapers are not in short supply these days. Spanish architects have proposed a 300-storey, 1,228m edifice for Shanghai. But the Saudi plan has done more to capture the imagination.

Prince Alwaleed – a nephew of King Abdullah of Saudi Arabia and an energetic disburser of oil wealth – is more likely than most dreamers to make good on his plans. He has already enlisted the Chicago-based architectural firm of Adrian Smith and Gordon Gill and it has designed something that looks like a paper aeroplane stood on end. (Mr Smith was the lead architect on Burj al-Khalifa.) Another source of fascination is surely that the Saudi Binladin Group will participate as a builder and investor. The announcement that SBG would help construct the world’s tallest building comes almost exactly a decade after another “bin Laden group”– Osama bin Laden’s al-Qaeda terror network – took the world’s one-time tallest buildings down.