The primary goal of this paper is to describe i) the pattern of pointwise distances between the human brain (pial surface) and the inner surface of the skull (endocast) and ii) the pattern of pointwise bilateral asymmetries of these two structures. We use a database of MR images to segment meshes representing the outer surface of the brain and the endocast. We propose automated computational techniques to assess the endocast-to-brain distances and endocast-and-brain asymmetries, based on a simplified yet accurate representation of the brain surface, that we call the brain hull. We compute two meshes representing the mean endocast and the mean brain hull to assess the two patterns in a population of normal controls. The results show i) a pattern of endocast-to-brain distances which are symmetrically distributed with respect to the mid-sagittal plane and ii) a pattern of global endocast and brain hull asymmetries which are consistent with the well-known Yakovlevian torque. Our study is a first step to validate the endocranial surface as a surrogate for the brain in fossil studies, where a key question is to elucidate the evolutionary origins of the brain torque. It also offers some insights into the normal configuration of the brain/skull interface, which could be useful in medical imaging studies (e.g. understanding atrophy in neurodegenerative diseases or modeling the brain shift in neurosurgery).