High-resolution scanning tunneling microscopy (STM) measurements on BaFe2As2-one of the parent compounds of the iron-based superconductors-reveals a (1x1) As-terminated unit cell on the (001) surface. However, there are significant differences of the surface unit cell compared to the bulk: only one of the two As atoms in the unit cell is imaged and domain walls between different (1x1) regions display a C2 symmetry at the surface. It should have been C2v if the STM image reflected the geometric structure of the surface or the orthorhombic bulk. The inequivalent As atoms and the bias dependence of the domain walls indicate that the origin of the STM image is primarily electronic not geometric. We argue that the surface electronic topography mirrors the bulk spin structure of BaFe2As2, via strong orbital-spin coupling.