The effect of misfit strain on properties of epitaxial BiFeO3 films that are grown along the pseudocubic ½ 110 direction, rather than along the usual [001] direction, is predicted from density-functional theory. These films adopt the monoclinic Cc space group for compressive misfit strains smaller in magnitude than ' 1:6% and for any investigated tensile strain. In this Cc phase, both polarization and the axis about which antiphase oxygen octahedra tilt rotate within the epitaxial plane as the strain varies. Surprisingly and unlike in (001) films, for compressive strain larger in magnitude than ' 1:6%, the polarization vanishes and two orthorhombic phases of Pnma and P212121 symmetry successively emerge via strain-induced transitions. The Pnma-to-P212121 transition is a rare example of a so-called pure gyrotropic phase transition, and the P212121 phase exhibits original interpenetrated arrays of ferroelectric vortices and antivortices.