You step into the glass lift and, for a minute, the city rearranges itself — streets and the Thames folding beneath you as the cab climbs at six metres per second. Sixty seconds later you emerge into the three-storey main gallery on Level 69, a bright ring of glass with an improbable panorama that stretches roughly 40 miles (64 km) on a clear day. For a raw wind-tinged experience, the partially outdoor Level 72 cuts you out of the building and exposes you to the elements amid the shards of glass that crown the tower.