The symmetry and existence ranges of GaSb and AlSb (111) A and B surface reconstructions are investigated using azimuthal-scan reflection high-energy electron diffraction (ARHEED) in a molecular-beam-epitaxy (MBE) environment. ARHEED patterns of all reconstructions within the accessible MBE group V flux-substrate temperature parameter field are presented and analyzed. The transition borders are mapped out as a reference for future growth experiments. The experimental results are interpreted on the basis of general construction principles for (111) surfaces of III-V semiconductors. ARHEED allows the complete determination of the two-dimensional in-plane reciprocal lattice in a single, continuous measurement. This allows the unambiguous identification of the reconstructions on (111) surfaces where the intrinsic symmetry is masked by the 120 • domain structure and possible disorder.