A ferroelec. and ferroelastic monodomain single crystal of BiFeO3 at space group R3c is rhombohedral, with a 5.57874(16), c 13.8688(3) .ANG.; arh 5.6343 .ANG., arh 59.348 Deg; d. (calcd.) = 8.337 for Z = 6. Final R = 2.4, Rw = 1.9% for 422 reflections. The structure can be described as a rhombohedrally distorted simple cubic perovskite cell. The O octahedron is distorted with min. and max. O-O distances of 2.710(7) and 3.015(9) .ANG., resp., and rotated by about +- a = 13.8(3) Deg around the 3-fold axis. The Fe atom is shifted away from the center of the deformed octahedron by .apprx.0.134(7) .ANG. along the 3-fold axis. The Bi atom is shifted with respect to 2 neighboring octahedron centers by .apprx.0.540(7) .ANG. along the 3-fold axis. The ferroelec. poling mechanism was analyzed: atom displacements were calcd. for 60, 120 and 180 Deg switching of Ps and found to be 0.44, 0.62 and 0.82 .ANG. for Fe. Av. oxygen displacements for +a (-a) rotated octahedra were 0.87 (0.89) 1.13 (1.24) and 1.34 (1.53) .ANG.. Av. Bi shifts were <0.06 .ANG.. As the displacements increase in the order 60, 120 and 180 Deg switching of Ps, the 180 Deg reversal must have a very high activation energy and will be avoided.