Prediction of low-energy phases of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Bi</mml:mi><mml:mi>Fe</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> with large unit cells and complex tilts beyond Glazer notation

We use density functional theory to identify several previously unknown polar and nonpolar structures within the low-energy phase space of perovskite-structure bismuth ferrite, $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$. Bismuth ferrite is one most widely studied multiferroic materials because its large ferroelectric polarization coexisting with magnetic order at room temperature. Of particular interest a series noncentrosymmetric along lattice vector, combined antipolar distortions, reminiscent domains, perpendicular direction. discuss possible routes stabilising new phases using biaxial heteroepitaxial strain or interfacial electrostatic control in heterostructures.