The Polikarpov I-13 was a design for a sesquiplane fighter aircraft produced during a period of some turmoil in the Soviet aircraft industry and that never progressed beyond the design stage.
Work on the design appears to have begun in 1931 while Polikarpov was working at TskB TaAGI (The Central Design Bureau, formed in 1930), under Sukhoi. This first aircraft was to be a sesquiplane fighter using a water-cooled inline V-16 engine. This is given as the M-32 in Gordon and Dexter's Polikarpov's Biplane Fighters' (Red Star 6), but that engine has proved difficult to trace and may never have progressed beyond the test stage.
The I-13 was intended to form part of a pair of aircraft designs, operating alongside the I-14 monoplane. The faster monoplane was to disrupt enemy formations and the manoeuvrable I-13 biplane would take advantage of the resulting confusion. Although neither of these aircraft designs reached production, the same concept was put in place using the Polikarpov I-15 biplane and I-16 monoplane.
Vaclav's Nemecek's 'History of Soviet aircraft from 1918' dates the I-13 to a slightly later period, 1933, by which time the TsKB become an independent body. Here the engine is given as the Wright Cyclone SGR-1820/F-3, an imported American engine. The upcoming I-15 would be designed around the Cyclone engine, and it would appear to be likely that some work was carried out on installing the new engine in the I-13 before work moved onto the newer design.