The former Saddam Hussein Gymnasium stands on the east side of the Tigris in Baghdad, next to Iraq’s national football stadium. It was built between 1973 and 1980 to designs made by Le Corbusier in the late 1950s. He also planned a giant stadium and other facilities in advance of a mooted Olympic bid, but only the gym was built. His designs for the Olympic project were on show at the V&A a few years ago, but City of Mirages: Baghdad 1952-82, at the Center for Architecture in New York until 5 May, puts the work in a larger context.