It is not entirely clear how the asymmetries of the skull and those of the brain relate to each other in hominids. However, in absence of well-defined landmarks on endocranial casts, it is common to use landmarks delineated on the skull to define a reference plane about which endocranial asymmetries are inferred, and to reconstruct a missing portion of an endocast with its "mirror image". The validity of these procedures is largely unknown. We investigate this question by defining and computing three different symmetry planes on several individuals. The first plane is computed by superimposing the outer (ectocranial) surface of the skull with its mirror image. This definition uses all the points of the surface, a probabilistic modeling of the latter, and the principle of maximum likelihood; the plane is ultimately computed using the expectation-maximization algorithm, and the whole procedure is fully automatic. The second plane is defined and computed in the same wa y, but using the inner (endocranial) surface of the skull. The third plane is the best-fit (using least squares regression) plane through a set of inter-hemispheric, endocranial, manually delineated landmarks. These planes are computed and compared in a quantitative way on two modern humans (young and adult), two modern chimpanzees (juvenile and adult) and one Australopithecus africanus (Mrs Ples, STS 5). Based on this study, a tentative virtual reconstruction of the endocast of the Taung Child, whose left endocast is mostly missing, is proposed.