Some evidence suggests that sex, handedness and disease processes associated with schizophrenia affect the magnitude and/or direction of structural brain asymmetries. There are mixed findings, however, on how these factors influence cerebral torque, when torque is assessed with linear or volumetric measurements. We obtained MRI data from 67 healthy (30 males, 10 non-dextrals) and 84 schizophrenia subjects (60 males; 16 non-dextrals) and applied cortical pattern matching to spatially relate and compare differences in the surface morphology of the two cerebral hemispheres at high spatial resolution. Asymmetry indices, computed at thousands of matched hemispheric locations, were used to examine effects of sex, handedness and schizophrenia on hemispheric shape asymmetries while controlling for age and the other factors. Highly significant and discriminative right-frontal and left parietal-occipital surface expansions and protrusions (petalias) were mapped within groups. Although hemispheric shape asymmetries appeared less pronounced within female non-dextrals, asymmetry indices were not shown to differ significantly across sex, hand preference or diagnosis, or to reveal interactions of handedness with sex or diagnosis. Our 3D maps of spatially detailed anterior and posterior hemispheric shape asymmetries reflect subtle geometric distortions in hemispheric surface morphology that cannot be characterized with 2D or volumetric methods. Inter-individual variations in hemispheric torque appear minimally influenced by sex, dextrality or disease status. Biological factors driving language dominance or other lateralized brain functions dissociable from handedness, may more closely relate to hemispheric shape asymmetries, while the lateralization of other discrete brain regions may be more influenced by sexually dimorphic factors or by schizophrenia pathophysiology.