Much of the variation in human personality is described by five to six dimensions. Less clear, however, is whether these dimensions are underpinned by similarly coherent and unified biological bases. Using the HEXACO traits, we tested whether genetic covariance within each dimension was underpinned by a single common genetic factor using three distinct classes of multivariate model. For each of the six factors, only a single common genetic basis was required to explain genetic covariation among the facets, along with facet-specific genetic effects. These findings provide support for personality models positing that the major dimensions of personality are each underpinned by a unified and coherent biological architecture.