The study is the first to analyze genetic and environmental factors that affect brain fiber architecture and its genetic linkage with cognitive function. We assessed white matter integrity voxelwise using diffusion tensor imaging at high magnetic field (4 Tesla), in 92 identical and fraternal twins. White matter integrity, quantified using fractional anisotropy (FA), was used to fit structural equation models (SEM) at each point in the brain, generating three-dimensional maps of heritability. We visualized the anatomical profile of correlations between white matter integrity and full-scale, verbal, and performance intelligence quotients (FIQ, VIQ, and PIQ). White matter integrity (FA) was under strong genetic control and was highly heritable in bilateral frontal (a(2)=0.55, p=0.04, left; a(2)=0.74, p=0.006, right), bilateral parietal (a(2)=0.85, p<0.001, left; a(2)=0.84, p<0.001, right), and left occipital (a(2)=0.76, p=0.003) lobes, and was correlated with FIQ and PIQ in the cingulum, optic radiations, superior fronto-occipital fasciculus, internal capsule, callosal isthmus, and the corona radiata (p=0.04 for FIQ and p=0.01 for PIQ, corrected for multiple comparisons). In a cross-trait mapping approach, common genetic factors mediated the correlation between IQ and white matter integrity, suggesting a common physiological mechanism for both, and common genetic determination. These genetic brain maps reveal heritable aspects of white matter integrity and should expedite the discovery of single-nucleotide polymorphisms affecting fiber connectivity and cognition.