The City & the City by China Miéville
Essay by Ted Gioia: http://www.postmodernmystery.com/the_city_and_the_city.html
Inspector Tyador Borlú, of the Extreme Crime Squad in the fictional European city-state of Besźel, investigates the murder of Mahalia Geary, a foreign student found dead with her face disfigured, in a Besźel street. He soon learns that Geary had been involved in the political and cultural turmoil involving Besźel and its "twin city" of Ul Qoma. His investigations start in his home city of Besźel, lead him to Ul Qoma to assist the Ul Qoman police in their work, and eventually result in an examination of the legend of Orciny, a rumoured third city existing in the spaces between Besźel and Ul Qoma.