Cross-sectional scanning tunneling microscopy is used to identify the origin of the anisotropic electronic structure of acceptor states in III–V semiconductors. The density of states introduced by a hole bound to an individual Cd acceptor in GaP is spatially mapped at room temperature. Similar to the Mn hole wave function in GaAs, we found a highly anisotropic, crosslike shape of the hole bound to Cd both at the GaP(110) and the GaP(1[overline 1]0) orthogonal cleavage planes. The experimentally observed similarity of the symmetry properties of Mn:GaAs to Cd:GaP shows that the anisotropic structure of acceptor states in zinc-blende III–V compounds is determined by the cubic symmetry of the host crystal. Nevertheless, the weak spin-orbit interaction in GaP leads to a slight modification of the Cd bound-hole wave function relative to that of Mn in GaAs. In addition to the anisotropic angular structure of the d-like spherical harmonic of the wave function, which dominates the appearance of the hole ground state far from the ionic core, the admixture of g-like and higher order spherical harmonics is identified at the sides of the Cd hole wave function. The experimentally obtained results agree with both atomistic tight-binding and envelope-function effective-mass theoretical models.