Leadenhall Building London

More commonly known as the Cheesegrater, this wedge-shaped 50-storey skyscraper opened in 2014 is angled at 10 degrees to protect views of St Paul's Cathedral, a legal urban-planning requirement. Most floors are office space, but you can dine mid-air at extravagant Bob Bob Cité, and the highest levels are sometimes open to the public during Open House London.